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Introductory books to Buddhism
I'm looking for some book(s) that are generally regarded as a good introduction to Buddhism. I know very little about Buddhism, having only read one book on it so far (What Makes You Not a Buddhist by Dzongsar Jamyang Khyentse Rinpoche). I found the book entertaining, but I'm not sure it was the best introduction for someone completely ignorant on the matter.
Are western takes on Buddhism - or at least books on Buddhism by western authors - a good way to start?
Or should one jump right into books like the Tibetan Book of the Dead?
What are some books generally regarded as good for a general introduction on Buddhism?

First off, I wouldn't recommend Tibetan Book of the Dead, since it's not exactly a primer in Buddhism, I don't think. There are lots of introductions from various traditions; the perennial favourite is What the Buddha Taught by Walpola Rahula. He's also written pieces on the difference (or lack thereof) between the various schools, so he's pretty unbiased that way.
Indian Buddhism by A.K. Warder is a great in-depth look at how Buddhism evolved, though like everything by the author it is terribly dense.
Bhikkhu Bodhi is another modern author who has some good resources; his introductions to the nikayas, e.g. in The Middle Length Discourses of the Buddha, are well-done. He also has an audio series on-line about the same that seems well-received.
I guess I'd be careful about modern sources either from the West or East as an introduction, since without a solid background, it will be easy to become swayed by skewed teachings. Reading the words of the historical Buddha himself would most likely help to provide such a background. Again Bodhi's translations are a good choice.

The complete PDF versions of a number of these books can be found here including What the Buddha Taught by Walpola Rahula, Indian Buddhism by A.K. Warder, the Connected Discourses and the Numerical Discourses by Bhikku Boddhi.

In the Buddha's Words by Bhikku Bodhi can be found here in full PDF

Quick First Read
What the Buddha Taught by Walpola Rahula (Recommended)
Good Question, Good Answer by S. Dhammika
Introductions to the Early Texts
In the Buddha's Words by Bhikkhu Bodhi
The Life of the Buddha by Ñāṇamoli Bhikkhu (Recommended)
Buddha-Dhamma for University Students by Buddhadasa Bhikkhu
Comprehensive Introductions to All Traditions
The Foundations of Buddhism by Rupert Gethin
The Buddhist Religion: A Historical Introduction by Richard H. Robinson
An Introduction to Buddhism: Teachings, History and Practices by Peter Harvey

I'll offer a controversial option, simply because it's the one that got me started (and in fact after reading it I don't believe the controversy is deserved). It's "Mastering The Core Teachings of the Buddha" (or "MCTB" by its fans) by Daniel Ingram .
Perhaps the main reason it is controversial is because Ingram gives himself the title "Arahat" on the cover of the book, and that is a decided no-no in many if not most Buddhist circles. However, I really encourage people to look past that. Ingram was doing it specifically to raise a controversial aspect, and even he says he has since had second thoughts about choosing to do it. The most important thing though is, the content of the book is utterly independent of his "arahat" claim. If you can see past that initial single word and actually read the book, you will find he is centered on pretty mainline, orthodox Mahasi Sayadaw style meditation practice, but also offers a broad and fairly deep understanding of other styles of Buddhist meditation too. Overall, I think the book is superb, but I'll offer three caveats for those who do decide to look past the arahat thing and read it.
First, the book is a bit too biased (in my non-expert opinion), on the Wisdom and Concentration aspects of the Eight-Fold Path, and doesn't pay enough attention to the Ethical conduct aspects. To be clear, he actually talks about ethics first, so in that sense he doesn't ignore it. But the bulk of the book is about how to meditate, and having now learned a lot more since I encountered MCTB, I think there's a danger of running into what B. Alan Wallace says in his Tsongkhapa commentary, "Balancing the Mind":
"Without a sufficient store of spiritual power [which comes from ethical conduct], meditation, such as training in quiescence and insight may arise as little more than barren, mental gymnastics that transform neither the heart nor the mind"
Second caveat: because the book is so good at explaining meditation in depth, there's a danger one could get "attached" to the attainments one may experience as one advances in practice. So instead of just sitting and noting, one could just get frustrated at apparent lack of progress. I believe that some teachers purposely do not give students too much advanced knowledge too early, precisely to avoid this problem. So if you're reading the book, be aware of this. Take your time, and don't fret too much about the fact you don't attain fourth jhana by day four!
Third caveat, and this is the most serious (much more of an issue than the "arahat" thing), is Ingram's focus on what he calls the "dark night". This refers to a subset of the stages of insight as described by Mahasi Sayadaw and others. I believe (I'm not that attained so I don't know) that what he is talking about is correct and it's very useful to know. But I also believe it is hugely over-emphasized. To be fair, it may be that it is Ingram's readers who create most of the over-emphasis, in various internet forums, but it's still a concern.
All that said, despite those caveats and the "arahat" thing, I still very much recommend this book. You can infer from that, that the good parts are very good (since they compensate for the caveats).

i recommend "The Heart of the Buddha's Teachings" by Thich Nhat Hanh
Good luck on your journey,
Tord

One of the classic introductions to Zen is Zen Mind, Beginners Mind by Shunryu Suzuki.
Bhante Gunaratans's Mindfulness in Plain English is widely cited as an excellent introduction to Vipassana meditation.

If you are interested in Vajrayana or Tantric Buddhism, I highly recommend the book by Reginald Ray titled, Secret of the Vajra World. He even covers a brief overview of other forms of Buddhism at the beginning, then dives into the Vajrayana.
It's very clearly written and covers a wide variety of the aspects of Tibetan Buddhist (Vajrayana Buddhist) practice and masters who teach and have taught it. In Vajrayana Buddhism, the lineage and the masters are an important part of the practice, via a practice known as guru yoga, where one learns to emulate the ideal of a buddha by practicing with one's teacher as an example.
This book is known as (marketed as?) a second volume in conjunction with the first (which is titled, Indestructible Truth) that covers other forms of Theravada and Mahayana Buddhism, however I found that the short intro to the Theravada & Mahayana in Secret of the Vajra World covered enough of that for me and that the other volume, though I read it, wasn't absolutely necessary, unless you are looking for a lot more detail on those earlier schools (and given your original question here, that first volume is probably in a LOT more detail than you'd like, for an introductory text).
In short, I cannot recommend highly enough Reggie Ray's book, Secret of the Vajra World as a "standalone" introductory text to Tantric Buddhism, if you're looking for an understandable and comprehensive introduction to a frankly, pretty complicated development of Buddhism, which is the Vajrayana.

Can I give a shout out for Jack Kornfield's excellent A Path with a Heart. I think it can be profitably read by a beginner or someone who has been practicing for many years. I've read it a couple of time I have every intention of reading it again.
I think it's also good to get into the actual original texts. Bhikkhu Bodhi is very good as said by yuttadhammo and he has an anthology In the Buddhas words which might be a bit less daunting than the Middle Length Discourses. Well it will be certainly easier to lift.
If you don't like 'best ofs' or compilations then the Dhammapada is accessible for an actual text. My current favourite is Eknath Easwaran
Anyway good luck with your reading

As mentioned in a some comments I would highly recommend In the Buddha's Words - An Anthology of Discourses from the Pali Canon (The Teachings of the Buddha) by Buddha Shakyamuni as compiled by Bikkhu Bodhi:

What better teacher can you find for an introduction to Buddhism than the Buddha himself? This is where I began and to my knowledge every extent tradition of Buddhism regards this book as authentic Buddhavacana.
If I had to pick one companion book to go with this which would explain the differences among the extent traditions of Buddhism in a thoroughly respectful and careful manner I'd pick Buddhism: One Teacher, Many Traditions by His Holiness the Dalai Lama and Venerable Thubten Chodron:

Hopefully the two books will give a solid introduction to Buddhism and Buddhist traditions.

I would like to recommend as introductory books

"Richard Gombrich: What the Buddha Thought"
The book is written by an English scholar. Gombrich does not consider himself a Buddhist but he expresses a high estimation for the Buddha's teaching.
The title of the book alludes to the title of the book by Rahula mentioned above. Rahula was one of Gombrich's teachers.
Two helpful textbooks for a course on Buddhism are
"Paul Williams: Buddhist thought. A complete introduction to the Indian tradition"
"Kogen Mizuno: Essentials of Buddhism. Basic terminology and concepts of Buddhist philosophy and practice."
A collection of texts, ordered by region and country
"John String: The experience of Buddhism. Sources and interpretations"
A critical reestimation, written as autobiography by a former monk:
"Stephen Batchelor: Confession of a Buddhist atheist."
The book is easy to read.

If you want a really challenging look at your own life as a starting point, you could try "Cutting Through Spiritual Materialism" By Chogyam Trungpa Rinpoche, an edited set of talks given in the early 1970's. He came from Tibet to the USA and saw that Western people need a very different approach to deal with cultural context and ego-psychology differences from the East. I think this is an important point.
I read it about 15 years ago, and recently began re-reading... It helped me all those years without me even being aware of it. Very powerful.

Despite the name (which I dislike), The Monk and the Philosopher is a great introduction to Buddhism from a Western point of view. It's a series of conversations between a French-Buddhist monk, Matthieu Ricard, and his father, Jean-François Revel, a philosopher. I found it more compelling than classical Buddhist texts, including some of the ones suggested here.

Another great pick for a Mahayana perspective! Could be mistaken since working from memory, but I think Mattieu Ricard was a member of the Padmakara Translation Group, source of the translation of Bodhicaryavatara that Pema Chodron comments upon in 'No Time to Lose.'

Lots of great suggestions above, but it looks to me like there's plenty of room to add a foundational Mahayana text to the mix. I suggest a complete presentation of the path in the form of a poem: Shantideva's "Way of the Bodhisattva" (Bodhicaryāvatāra).
An especially poetic translation with commentary that helps make the immediate practical value of this text evident (omitting the very challenging 9th Chapter on the perfection of wisdom, which is really hard going if you're looking for introductory material anyway) is in Pema Chödrön's No Time to Lose -A Timely Guide to the Way of the Bodhisattva. There are excellent materials that convey some of the functions of this text in Indo-Tibetan Buddhism, along with translations of the first 3 chapters, freely offered by Lotsawa House.
It's also certainly worth hearing commentary from the Dalai Lama on this text, who has said: "If I have any understanding of compassion and the bodhisattva path, it all comes from studying this text." (Cited from RigpaWiki) These teachings may be a little more challenging for a beginning student than No Time to Lose, but I think they are still immensely helpful and accessible commentaries for those who feel inspired by this extraordinary work. Maybe start with For the Benefit of All Beings.
May the studies of all students of Buddhadharma bear the fine fruit of realization!

Above recommended books are very good.
Also you can compliment the above list by adding books by Thanisaro Bikku who has done some good translations.
Main thing is to always cross check with the source as the Venerable Sir points out.

Venerable Narada: The Buddha and his Teachings
The Dalai Lama: The Way to Freedom
Dzongsar Khyentse Rinpoche: What Makes you not a Buddhist
Robert Wright: Why Buddhism is True
The Dalai Lama: A Profound Mind

Most of the books are already mentioned and many of them are really good introductory books.
I have one more to add. Its called "What Buddhists Believe" by. Ven. K. Sri Dhammananda.
In here he discusses e.g. "The Life and Nature of the Buddha, His Message, Basic Doctrines, The Tipitaka, Kamma, Morality, Rebirth, Nibbana, How to lead a buddhist life and much more". The book is highly recommended.
Also here is a Buddhist Dictionary - Manual of Buddhist Terms and Doctrines  by Ven. Nyanatiloka.
Lanka

Good start! if you find Rinpoches Dzongsar Khyentse teachings attractive then i would suggest listening to his teachings on Utube as there are many on there for free. Also, what i do is go a library or book store and investigate different books for myself and that seemed to work best.

Buddhism is about meditation. Learn to meditate first. Then try to understand Buddhism.
This was my method (and two books I highly recommend): learn the shortcomings of Vipassana/ mindfulness; and then try absolute samadhi meditation, or Jhana, or Zazen.

Mindfulness, Bliss and Beyond (by Ajahn Brahm)
On the subject of Meditation (Vipassana vs Jhana), Ajahn Brahm wrote an excellent book called Mindfulness, Bliss and Beyond. His central thesis is that without Jhana there is no enlightenment, he also said it was jhana not Vipassana that led to the Buddha's awakening. I have to agree with him.
Seventeen years ago I started Vipassana (mindfulness) meditation and although it's a good foundation. I didn't progress very far.
When I started studying and practicing Zen, especially absolute samadhi meditation as taught by Katsuki Sekida, this is when I began to truly understand the Buddha's teachings.
I would add that Jhana, Zazen and absolute samadhi meditation is the same form of meditation: based on letting go... with focused concentration/absorption in the moment. Vipassana/Mindfulness is a continuous use of noting, but not absorption, because it would be impossible to do. That's the difference between the two methods of meditation. Absorption in the absolute moment leads to consciousness falling away. The beginning stages of the awakening process.
Zen training (methods and philosophy) (by Katsuki Sekida)
Katsuki Sekida wrote a book called Zen training (methods and philosophy). I would get it, along with Ajahn Brahm book, as it definitely will help you. I guarantee it will deepen your understanding of meditation and Buddhism. I know in my own practice learning to let go of all conceptual understanding, thinking, and just let things happen, is when the magic appears in meditation, or I should say drops off. Waste of time talking about Buddhism. Buddhism is a very personal practice...absolutely no one can help you. Making it into a religion destroys it. All that really matters is the meditation.

All the best
M

The trilogy "Approaching the buddhist path" is not only a good starter, but also a good companion for "advanced" disciples.
I also would give YouTube a try:
The Buddha is a very good starting point with interesting commentators.
You can also check the learning modules from Discovering Buddhism
And it is always a pleasure to watch Dzongsar Khyentse Rinpoche ("What makes you not a Buddhist")
Enjoy

To the already very useful answers, I would like to add Joseph Goldstein's excellent book, Mindfulness: A Practical Guide To Awakening.
He explains Buddhism from the perspective of the Satipatthana Sutta, so there is a huge focus on Mindfulness, but he does explain (very well) the Four Noble Truths and The Eightfold Noble Path as well.
As the title explains the book is very hands on and practical in working with the mind, while also explaining enough of the theory that's required.
I am still reading this book, but am really delighted with everything I have read.

I think the best primer is introduction to general semantics such as 'Stuart Chase; Tyranny of Words' available as free pdf.
That i think because the initial training in the general system of language in itself challenges the notion of self and allows for easier understanding of Buddha's system of language and what it is one is dealing with.
After that i think on should read according to one's inclination. Some would read poetry and some would want to discuss the Dhamma. To make sense of the points of controversy one would preferably want to have at least general knowledge the sn, mn, an, dn, ud, dhp, snp, vsm, abh this is even for the sake of expression alone is something one would want to have knowledge of to communicate effectively.
Therefore i think it is best to just start somewhere. Just get through content one way or another with a system of critical thinking in place and start building the understanding.

In the order of reading:

The Four Noble Truths - Ajahn Sumedho
Transformation and Healing: Sutra on the Four Establishments of Mindfulness - Thich Nhat Hanh
Breathe! You Are Alive: Sutra on the Full Awareness of Breathing - Thich Nhat Hanh
Awakening Loving-kindness - Pema Chodron
Mindfulness, Bliss and Beyond - Ajahn Brahm
The Dhammapada - Eknath Easwaran

Tibetan Book of the Dead is the jewel of Nyingma school of Tibetan Buddhism and Vajrayana, and that is, therefore, a tantric path of Buddhism. Since tantra isn't the path of renunciation it is not an entirely Buddhist path, since its being selective about Buddha's teachings introducing many Hindu concepts to it. No, it is not good introduction to the core of Buddhism teaching, or Buddhism at all, it explains concept of Bardo that is non-existent in Theravada and original Buddhist canon.


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The spiritual significance of the sand mandala in Tibetan Buddhism
I have heard of and seen sand mandalas in Tibetan Buddhism.
Here is a picture:

I have two questions, which are related:

I have heard that upon completion they are erased to represent transience. Is this what the erasure represents?
What other spiritual significance does the mandala have in Tibetan Buddhism. I seem to remember something relating to a spiritual journey being represented in the mandala yet I am unsure. I would like clarification on this.

"Mandala" is not always "sand mandala". First, it may be done using media other than sand. Second, "mandala" in its wider meaning stands for configuration or layout of components comprising a context. For example "While not being a public figure, his wife clearly occupied a key place in Chogyam Trungpa's mandala".

According to The Tibetan Monks of Drepung Gomang Monastery

When finished, to symbolize the impermanence of all that exists, the colored sands are swept up and poured into a nearby river or stream where the waters carry healing energies throughout the world.

In general, all mandalas have outer, inner, and secret meaning.  On the outer level they represent the world in its divine form; on the inner level, they represent a map by which the ordinary human mind is transformed into the enlightened mind; and on the secret level, they predict the primordially perfect balance of the subtle energies of the body and the clear light dimension of the mind.  The creation of a sand painting is said to affect purification and healing on these three levels.

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What is the purpose of using a wand to hit a monk in Zen meditation?
I have seen Zen monks in meditation, usually with one monk supervising. The monk supervising usually carries a wand of some sort. Every once in a while he would rest the wand on the shoulder of one of the monks and then respectfully hit his shoulder. It did not seem very forceful yet I found this confusing because to me it seemed as if it may be a method of harm or violence. I would like clarification on this practie.
Why does the supervising monk do this to the meditating monks?

Supposedly it is used to help meditator fight drowsiness. It is said that drowsiness comes from stiffness, from meditator trying to artificially restrict their micro-movements and to severely narrow their scope of attention. While right concentration is said to feel open and flexible, with body actively balancing in meditation posture and attention wide open (but not engaged nor scattered). When supervising monk sees somebody nodding, he reminds meditator of the need to expand their awareness, by gently "massaging" the shoulder with the stick :)

During a weekend retreat I attended at a Zen monastery, the explanation I heard was that the sensation provides a point of focus for meditation.  At this monastery (or at least at this retreat, which was for beginners), receiving a hit from the wand was voluntary; I don't think they used it to wake up participants.
Other sources (including other answers to this question) have suggested that waking up a dozing meditator is another use.

It's a remedy for sleepiness. Nothing special. It's a little pat on the back to keep you awake.

this sounds right, but it's always nice to have answers that provide some detail/background... can you provide us with some more information about the practice?

Ven. Yuttadhammo: In this case, a laconic answer seemed appropriate. If I am asked "What is the purpose of condoms?" I will answer: "It is to reduce the probability of pregnancy and STDs." - That's all there is to it, there's no need to go into the history of the condom, who invented it, what the Church and the Pope think about it, etc., because the question is asking about the function or the purpose of the item discussed. Does this go against the Stackexchange ethos?

Yes, it really does... SE is an expert exchange; the idea is to give expert answers. See our meta discussion here: http://meta.buddhism.stackexchange.com/questions/26/should-we-allow-encourage-short-enigmatic-answers?cb=1

Thanks Ven. yuttadhammo, I see the problem. My answer was not enigmatic or "Zen-like", though. I simply described the tool's function. I lived in a Zen temple for some time, and I believe there's literally nothing else to add. But in the future, I will avoid answering in such situations, to avoid giving the impression that I'm being purposefully enigmatic or dismissive(?) or something to that effect. Thanks for the heads up.

I wasn't trying to imply either that you were enigmatic or dismissive, just brief. See the answers to this question: http://meta.stackexchange.com/questions/138738/should-i-give-short-answers-or-comments especially "We want to Make The Internet Better(tm) with good answers that explain the issue, and help everyone learn--the visitors and the OP alike."

+1 -- and if you had wanted to add something, perhaps a link to a worthwhile source/reference which confirms what you said.

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What is the difference between rebirth and reincarnation?
In my readings of Buddhist commentary there is a distinction drawn between rebirth and reincarnation. But to me it is unclear what is the difference between rebirth and reincarnation--the explanations are rather abstruse. Is there a simple one-sentence explanation of this difference?

It would be great to have the precise terms in original language, that would make it much easier to answer. Can you provide them?

i downvoted the answers cos they don't say why 'reincarnation' implies a soul

now i wish i had not, but cannot reverse my vote. my question here should i hope answer the question i've posed more thoroughly

Reincarnation implies a soul that takes a body; rebirth does not, so it is preferred.
Note that neither term has a widely used cognate in the Pali texts, perhaps because the concept of "re-" anything implies the continuation of an entity. Buddhism tends to talk about birth and death in a more linear fashion; rather than being reborn, it's "being born again" (e.g. dukkhā jāti punappunaṃ).
Further, the focus in Buddhism is on individual mind states and ultimate reality rather than the conceptual reality of birth and death, so it's not really a core teaching. Death is a concept; at the moment of a being's death, one body/mind experience ceases and the next one arises, just as it did through the entire life.

The Buddhist Pali word 'birth' ('jati') refers to the arising of the self-view of 'a being' ('satta').

And what is birth? The birth of the various beings into the various orders of beings... SN 12.2
'A being,' lord. 'A being'. To what extent is one said to be 'a being'? Any desire, passion, delight or craving for form... feeling... perception... fabrications... consciousness: when one is caught up there, tied up there, one is said to be 'a being.' SN 23.3
Why now do you assume 'a being'? Have you grasped a view? Just as with an assemblage of parts, the word 'chariot' is used, when the aggregates are present, there is the verbal convention of 'a being.' SN 5.10

The many different Pali words translated as 're-birth' essentially refer to the re-arising or re-formation of the self-view of 'a being' due to kamma (action).
For example, under the influence of self-view, a person undertakes a financial scam & celebrates when they become or are 're-born' financially wealthy. Then, when they are imprisoned for fraud, the same person is re-born as a prisoner in a jail & are unhappy.
In summary, despite the different interpretations, 'rebirth' is always a doctrine of 'moral efficacy'.
Where as 'reincarnation' is always a metaphysical doctrine of the soul or some other mental substance entering a new physical body.
A Buddhist can believe in moral 'rebirth' but not believe in 'reincarnation' (life after death).

Reincarnation involves a soul that transmigrates. A soul is the five aggregates minus physical form.
Rebirth is like lighting one candle with another candle. The stream of consciousness, a.k.a life force, continues from one existence to another but the remainder of the five aggregates; form, perception, sensations and mental formations (which would stay together during a reincarnation of a soul); dissipate.

Rebirth is when a soul leaves the body in the state of ignorance and then again gets a new body in ignorance.
Reincarnation is when soul leaves the body in full knowledge and such souls reincarnate only to fulfill a some mission or purpose in life.


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What, precisely, is kamma/karma?
In Buddhist doctrine there is always the problem, that for the sake of understandability, certain concepts are being presented in a solid, substantial way, while actually, one has to keep in the back of one's mind, that by the central tenet of anattā/anātman these concepts are actually not like that. The same applies to kamma/karma, which can be presented as something that a being accumulates and carries with itself in this life and to the next and the ones following.
Now, actually, there is nothing substantial that transmigrates from one life to the next, as is clear from the similes that are used to explain rebirth without soul: a candle that lights another, an echo, a mirror image, the imprint in wax of seal. In these cases, though there is some link between the two sides, nothing actually goes from one to the other (the case with the echo should maybe be reconsidered according to the old Indian theories of sound and the echo). So, what is kamma/karma? How does it stick to the individual?
To take this question one step further, if we admit now that kamma/karma is near-identical with the concept of saṃskāra/saṃkhāra, and therefore with volitions and cetanā, as in this quote from AN 6.63:

cetanāhaṃ bhikkave kammaṃ vadāmi
Intention, I tell you, is kamma

and that by karmic unwholesome action the consciousness "leans towards" unwholesomeness, then how are these leanings supposed to look, how are they thought to be transported from one conscious moment to the next?

If I'm not mistaken it is the thought category called javana which carry the thoughts along.

There are two main interpretations of how karma is accumulated.
In Sarvastivada branch of philosophy, past actions can be directly related to new consequences, because fundamentally "everything exists" and only the modus of time changes. As things aren't losing the status of existence, they can cause new things. There is a special additional property (called prapti) to relate or un-relate action to the stream of consciousness. So when you perform an action it doesn't need anything else to be able to cause karmical fruit. (Of course it requires other conditions to work.)
In Sautrantika branch of philosophies, actions are accumulated by means of traces (bija-vasanas) in some sort of storehouse consciousness (alaya-vijnana). It works similarly to when you plant the seed of a tree into the ground; the seed disappears but the tree still contains the ability to ripen into certain fruits. Thus, action could be accumulated in something completely different from the action itself. So when you act, you actually change yourself as a whole in a way that accumulates the potential to acquire karmic fruit.
Yes, intention is kamma, but there are two types of kamma (SN 35.145) old kamma and new kamma. Where new kamma is intention (as thinking) and what-is-after-intention (actions of speech and body), while old kamma is your body as whole (i.e. the totality of all organs). In that way you have your old kamma always with yourself in your body (including all organs of perception and intellect).

I have to comment and say that this answer doesn't really clear anything up for me.

Karma is not something one accumulates; this question gets asked so often because, as you say, there is a misconception of it being a 'a solid, substantial' entity.
Karma is volition (intention is a bad translation, IMO), or in abhidhamma, the seven javana citta present in an ordinary mind process (i.e. every moment of experience).
All this means is that every experience you have has the potential to affect future experience in some way; the fact that karma produces a result in kind is indicative of how natural the process is - karma is simply the law of causality that moulds our lives according to our actions. That this should continue after death is not a problem for Buddhism since, as I've noted several places here already, death according to Buddhism is just a concept. The mind states continue to arise and cease according to the law of causality.
As to how one mind can affect the next, I really have no answer besides that through the practice of meditation you can verify for yourself that it is indeed the nature of reality; why it is this way is somewhat irrelevant.

Btw, it may follow from your answer that in Abhidhamma there is 'javana citta' instead of 'cetana'. But even in Abhidhamma kamma is cetana. While 'javana citta' is just 'impulse of consciousness', and not replaces 'cetana'. Each 'javana' have its own 'cetana' to account for kamma.

Another way to look at it is, Karma is "what is happening" in the sense of ripples on the surface of water, where the center of each ripple is Karma, and every interaction of each ripple makes a new center, which is Karma. Like ripples in water, Karma does not, strictly speaking, exist as  a thing unto itself, but as a pattern that can be observed only by inference.

A lot has already been said about the intention part of what kamma is.
I just want to add something on how 'things' get transported to the next mind moment.
If you want to know how that works you really have to dig into the different paccayo's as discribed in the Patthana.
In this case the
Kamma Paccayo.
Important to remember is that there is never just one paccayo at work. There are always several paccayo's working in a moment having impact on the object or the next mind moment or...

What, precisely, is kamma/karma?
There is no answer to the above question:
Kamma is not in the Oxford Dictionaries. Thus its meaning is dependent on the user.
Karma is defined in the Oxford Dictionary, thus:
Definition of karma in English:
karma
1[mass noun] (in Hinduism and Buddhism) the sum of a person's actions in this and previous states of existence, viewed as deciding their fate in future existences.
Wikipedia defines it as follows:
Karma (Sanskrit: कर्म; IPA: [ˈkərmə] ( listen); Pali: kamma) means action, work or deed;[1] it also refers to the spiritual principle of cause and effect where intent and actions of an individual (cause) influence the future of that individual (effect).[2] Good intent and good deed contribute to good karma and future happiness, while bad intent and bad deed contribute to bad karma and future suffering.[3][4] Karma is closely associated with the idea of rebirth in many schools of Asian religions.[5] In these schools, karma in the present affects one's future in the current life, as well as the nature and quality of future lives - one's saṃsāra.[6]
With origins in ancient India, karma is a key concept in Hinduism, Buddhism, Jainism, Sikhism,[7] and Taoism.[8].
There is no precise definition for Karma.
The word Kamma is not found in the Nikaya Texts of Theravada; however, it is found in compounds.
A word kammaṃ is found in the Nikaya texts. The words cetanāhaṃ bhikkave kammaṃ vadāmi is an example of usage. The meaning of the word is not understood is clear from the discussion.

There are two types of kamma or deeds.
1).Meritorious deeds

They are described as deeds which generate peaceful pleassure in mind.
  Effects are given as peaceful pleassures with less attempts

2).Demeritorial deeds

They are described as deeds which generate harsh and suffering in mind
  even at the moment of kamma. Effects are given as suffering with no
  results even with hard attempts.

Hey, it would be great if you could provide some sources.

To understand correctly anattā teachings, we have first to determine what exactly is Something according to Buddha and Buddhism.
Something , or positive value, according to Buddhism is 5 skandhas, 12 Āyatanas or 18 Dhātu, i.e. - all perceivable reality - and that is indeed what doesn't reborn.
Buddhism is here inline with Upanishadic teachings on Ātma - which defines: "Ātma is naught" , "Neti, neti" - "Nor this nor that", "Only naught exists" - it is nothing which could be included in our empirical perception, but still it exists, or otherwise - you cannot tell exactly not that it exists, not that it doesn't...
Sadly enough there are many misconceptions on this subject today among people - since there would be different experiences of those clearly perceiving the inner light and those living in ignorance...
Regarding Karma I agree with what was said earlier - on one hand - Karma is vasanas or impressions in the consciousness, or Alaya-vijnana, created by the our Activities - Wrong action, speech or thought - since the word "Karma" itself means Action, Activity in a wider sense.

On the other hand, from the absolute viewpoint of realization of Buddha-mind - those impressions in the mind are as much "real" for the Liberated as the reality of Anatta or ego itself, as much real as all 5 skandhas perceived by the ego, who is not real actually.

So - from the Absolute viewpoint "only naught exist" - nor mind, nor karma, nor Ātma nor perceptions, nor feelings, nor categories have a real being.... They are just a mud hiding from us the ever shining Buddha mind, alas god in other religions...
No wonder in Sanskrit both - Buddha and incarnations of God - are addressed equally - Bhagavān - translated by Buddhist authors - as Lord - and translated by Krishnaits - as "The Divine Personality of Godhead":)
But let's remember - for ordinary people, who are not reached the absolute Liberation yet, not all affections and ignorance is cleared yet - "Everything exists" - meaning all 5 Skandhas exist, and they are quite "real" for an ordinary citizen and cloud their perception and intentions.
Regarding the definition - that "Karma is intention" - I would remind the old simile of Buddhist Arahants - in their answer to the quetion - "How did god create this universe - with intention or without?!" - The answer, according to tradition was - "If he had an intention - he was selfish, he got some selfish motive. And since - he would not be regarded as an Absolute. In case - he didn't had any intention or motive - we say: he is probably playing as a small kid...":)


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Is it harmful to the Buddha when we request he or she to continue teaching instead of entering parinirvana?
One of the ten things that Bodhisattva Samathabhadra says that a person on the Bodhisattva path should do is to request the Buddhas to continuing teaching instead of entering parinirvana. Given that a Buddha is fully compassionate and omniscient, he or she would want to teach if doing so is beneficial to sentient beings and would also be aware whether teaching is indeed beneficial to sentient beings. For example, the historical Shakayumni Buddha wanted to enter parinirvana because some of his sangha was becoming complaent that they would always have  the Thus Come One as their teacher. As such, it would seem that a Buddha would be able to decide well the timing of his parinirvana.
Given the above, I wonder how would it is appropriate for one learning to walk on the Bodhisattva path to request the Buddhas to continuing teaching. Is such an action for the benefit of the practioner to generate a wish of englightment and to take refuge in the Buddha? Does a Buddha need to enter parinirvana at a certain time, otherwise it would become harmful to him or herself or to the community at large? Is a Buddha unable to stay longer to teach if practitioners do not make requests? (Sorry that I am unable to phrase a precise question, but I hope I conveyed my gist and my confusion clearly enough.)

As I pointed out in my answer to "are earthworms our mothers?"  these kind of questions often assume incorrect frame of reference. The reason we request Buddha (or our local teacher as Buddha's substitute) to continue teaching instead of entering parinirvana, is not because it can literally make Buddha (or teacher) change their mind and stay. The idea is to create a mental context in which A) the teacher feels motivated to continue teaching because he sees the teaching is in demand, B) the students stay aware of the fact that existence of the teaching in this world depends solely on Buddha and then generations of teachers passing it to one another, and now to the students, and C) the student clearly realizes that the teacher could very well leave this place but is instead making effort to stay and teach solely out of compassion for the students. When this context is established the teaching can happen effectively, because both the sides will engage actively and with no resistance.
Granted these are entry-level practices, but they are very important to establish as foundation. Otherwise what happens if you skip straight to advanced teaching, the student may get as arrogant as to metaphorically grab the teacher by the hair and swing around. Needless to say, it hurts the student first and foremost.

I'm not sure I understand your question(s) fully; however, since you seem to be coming from a Mahayana background, do remember that the Lotus Sutra reveals Buddha's entering parinirvana is merely an expedient device. He merely appears to enter parinirvana to "motivate" people, as it were. According to that Sutra, which claims to be the ultimate and true teaching of the Mahayana, the Buddha doesn't enter parinirvana but instead eternally abides in this world.

All Buddhas are masculine. No, it is not harmful to invite the Buddha. In fact, the Buddha mentioned several times that a person who has perfected Sathara Iddipada can live the maximum life span of a human at that time. It was about 120 years back then. So he could've stayed another 40 years had he been invited. Venerable Ananda had several opportunities to invite the Buddha. But it's said that Mara(the evil god) prevented him every time.


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Do Arhats sleep?
I have read somewhere that Arhats (people who attained Nirvana) do not sleep like normal people do. Instead they just stay calm in a suitable position to give the rest required for the physical body, but their mind is always alert...
Is this true?

According to the teachings I received, once the practitioner attains certain level of mastery in meditation, their sleep acquires a character of meditation. It's not like they don't sleep at all, but they do retain certain level of deep awareness during their sleep.
Specifically, when they see a dream, they know it's a dream. They remain aware of their body lying down on the bed. They remain aware of the content of their consciousness no matter how disjointed it gets during a deep sleep. If something happens around them, they wake up easily to provide their help if needed.

The Buddha is reported not to have slept, but teaching ceaselessly and just entering a state of meditation for two hours per day/night. I don't have any scriptural evidence for this and am rather sure, that none such evidence exists.

Can you please give the source..?

Nice answer. Any chance you could point us to a scriptural or other source about the Buddha not sleeping?

But please note that the Buddha and Arhat are two difference stages

According to this article, The Buddha sleep only one hour

@PasanW, senshin: There is no written source to this. As I was trying to indicate with the words "is reported" - well, maybe not quite clearly - is the fact, that this is just a tradition. I edited the answer to make this point clear.

An Arahat does not sleep like a normal person. He may give rest to the body but in doing so is fully aware hence not asleep. This is a natural consequence of reducing impurities of the mind. Also the level of awareness does not change.

Another enemy is laziness, drowsiness. All night you slept soundly, and yet when you sit to meditate, you feel very sleepy. This sleepiness is caused by your mental impurities, which would be driven out by the practice of Vipassana, and which therefore try to stop you from meditating. You must fight to prevent this enemy from overpowering you. Breathe slightly hard, or else get up, sprinkle cold water on your eyes, or walk a little, and then sit again.
...
Similarly, when you go to bed at night, close your eyes and feel sensation anywhere within the body. If you fall asleep with this awareness, naturally as soon as you wake up in the morning, you will be aware of sensation. Perhaps you may not sleep soundly, or you may even remain fully awake throughout the night. This is wonderful, provided you stay lying in bed and maintain awareness and equanimity. The body will receive the rest it needs, and there is no greater rest for the mind than to remain aware and equanimous. However, if you start worrying that you are developing insomnia, then you will generate tensions, and will feel exhausted the next day. Nor should you forcefully try to stay awake, remaining in a seated posture all night; that would be going to an extreme. If sleep comes, very good; sleep. If sleep does not come, allow the body to rest by remaining in a recumbent position, and allow the mind to rest by remaining aware and equanimous.

Source: The Discourse Summaries by S.N. Goenka
Also see: Suppati Sutta

After first attainment , i had entered into sleep while meditating for 3 times.
When i entered into dream i had aware that i am entering into dream, there once i have entered dream , i notice horrfying events in full awareness, i notice each event in dream as it is and then finally everything gone , i was left in  a empty space-like state still meditating till i woke up. It is very fascinating event.
So i can understand what will be arahant like , it is not dreaming anymore , it is mediation while in sleep.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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What are the major sects of Buddhism?
Every major religion has several different belief systems (sects) that have the same general core belief, but have a significant enough different to have be separated from each other.
What are the major (3-10) sects of Buddhism?  How are they different from each other?

I follow the SGI. Its roots are from the lotus sutra

Mahayana is not a sect at all; it is a vehicle.
Major traditions in Buddhism are usually country or region related. We can distinguish three major branches of Buddhism in the World by what they keep as canon.

Tibetan, Mongolian, and Russian Buddhism share Tibetan canon.
Chinese, Japanese, and Korean Buddhism share Chinese canon.
Sri Lanka, Burma, Thailand, etc share Pali canon.

Some countries mix several aforementioned branches.

catnpnosis, you used the word "branches" in your answer: is "branch" different from "sect" and "vehicle", or were you using it as a synonym for "sect"? If the latter, your answer would be clearer if you replaced "branches" by "sects" (or at least clarified that they were the same thing.)

FYI, Wikipedia refers to Mahayana as both a vehicle and a branch: http://en.wikipedia.org/wiki/Mahayana (which would further suggest that when you said "branches" you really meant "sects", no?)

@Tommy I used branch as most general division (plus, it's neutral), and 'sect' copied from the question, actually, not very correctly. Sect is loaded term, it supposes more organized / centralized unit, or even smaller schools. I will edit and replace 'sects' in my answer with 'traditions'. Thanks.

More or less these geographical and linguistic entities coincide with the different vehicles.

@zwiebel They don't.

Elaborate if you don't mind.

@zwiebel Chinese and Japanese Buddhism have Buddhist Tantra as well as Nikaya sutras. Tibetan Buddhism have both Mahayana and Vajrayana teachings on par (while studying Hinayana schools too). Both also have 'early school' vinaya lineages. South Buddhism have Bodhistattva teachings, and even some parts of Theravada could be classified as Mahayana (for example teaching on the emptiness of dhammas, ch.XX of Patisabmhidamagga, which some schools interpret as signature of Mahayana). I think it's never correct to assign single theoretical philosophical view to real schools or persons.

Well still, if you just look at the canons, they more or less coincide. Of course it's not black and white, but I never claimed this. And you're right (maybe everywhere so, maybe esp. in Buddhism), that it is impossible to assign easy identifications, for example for what is Mahayana and what not. But since this is not possible, even more so do they more or less coincide...

Half of Chinese canon is Agama (Nikaya) sutras which is not Mahayana at all. Half of Tibetan canon is Mahayana scriptures which is not Vajrayana at all. And Pali canon is not only corpus of Theravada. Most popular Japanese Buddhism is Vajranaya schools. And there is nothing Mahayana in vinaya traditions of both Tibetan and Chinese Buddhism. To coincide, with such tremendous differences, regional Buddhist traditions to yanas is extreme simplification.

The three major sects would be Hīnayāna - the small vehicle/path; Mahāyāna - the great vehicle/path and Vajrayāna - the diamond vehicle/path. For differences compare this thread: What are the main differences between the Theravada, Mahayana and Vajrayana branches of Buddhism?


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Is there an Orthodox Buddhism?
Orthodoxy in Christianity is the holding to the oldest beliefs.  It is of course impossible for the religion not to evolve at all as new questions and there answer have to addressed. The "Orthodox" version is often considered to be the least evolved sect of a religion.  Does the concept of Orthodox apply in Buddhism?

Yes. The Mahavihara tradition claims it is the Orthodox while some are reluctant to accept. It is natural for both sides.

Well, Theravada is often argued to hew most closely to the original teachings of the Buddha. See, e.g. "Two Main Schools of Buddhism" for a very brief overview of this.
As I understand it, this has much to do with the fact that Theravada is the oldest of the extant Buddhist schools of thought, predating Mahayana by a few centuries. Theravada practice is also more localized to geographic regions nearer the birthplace of Buddhism (that is, Sri Lanka and Southeast Asia), and never strayed far from it; this is thought to have contributed to the "orthodoxy" of the school - it mixed less with other intellectual and spiritual traditions.
Additionally, Theravada Buddhists draw primarily on the Pali Canon (the Tripitaka), whereas Mahayana Buddhists draw primarily on Chinese sources. These Chinese sources are relatively more distant from the original teachings of the Buddha in terms of both time and language. As a byproduct of this, the Pali texts are often more "authentic".1
That said, the term "Orthodox" has no specific meaning in the context of Buddhism, i.e. there is no such school as "Orthodox Buddhism". There are only lowercase-o "orthodox schools of Buddhism", and what counts as "orthodox" will probably differ depending on who you ask. I should add that pre-sectarian Buddhism is almost definitionally the most "orthodox" school of Buddhist thought. The only problem is that, well, it doesn't exist anymore.

1 See, e.g. Rupert Gethin's The Foundations of Buddhism, p. 44: "it is likely that [it] is generally the case [...] that the traditions [the Pali recension] preserves are [...] the oldest and most authentic available to us" (elisions/etc because the original sentence was inverted)

"Predating Mahayana": There is a tendency to connect Theravada with the ancient Sthaviras that separated from the Mahāsāṃghikas, but that's not necessarily true. Theravada is definitely connected with the Mahavihara of Sri Lanka but their doctrine may not necessarily go back to the Sthaviras. Theravada either goes back to 400 BCE with the Sthaviras, or 300 BCE with introduction to Sri Lanka or later as Theravada developed itself and gained ascendency in Sri Lanka in 1200 CE. If so Mahayana might actually be older.

@CalebPaul are you a Mahayanist?

@senshin: Why does this not become another Unorthodox view? Or another sect like Theravada, Mahayana? How does Rupert Gethin be the ultimate judiciary in this matter? How does it differ from another Personal Opinion?

There is no Orthodox Buddhism, there is Traditional Buddhism. Most modern traditional branches of Buddhism with monkery, root in some or other ancient school. Theravada is not more Orthodox or ancient than most other traditional schools.

Is this evidence-based or just another speculation?

Orthodox Buddhism would be what we call Pre-sectarian Buddhism, which does not exist any more, as a tradition or school or sect. Pre-sectarian Buddhism split into the Mahasamgika school and the Sthavira school.
The modern Theravada tradition, is probably the closest modern school to Pre-sectarian Buddhism, in terms of its doctrines. Theravada is based on the Sri Lankan Mahavihara school, which descended from the South Indian Tamraparniya branch of the Vibhajyavada school, which descended from the Sthavira school.
In this blog post, Ven. Sujato wrote:

The term sthavira (meaning ‘elder’) is the Sanskrit version of the
term better known today in its Pali version thera, as in Theravāda,
the ‘Teaching of the Elders’. The original Sthaviras, however, are
by no means identical with the modern school called Theravāda.
Rather, the Sthaviras are the ancestor of a group of related
schools, one of which is the Theravāda.

To me, the most orthodox teachings of Buddhism are found in the Theravada Sutta Pitaka and the Mahayana Agamas, which are essentially the same thing.
Personally, I don't consider the Theravada Abhidhamma and the later Mahayana Sutras (like the Lotus Sutra or Heart Sutra) to be orthodox.

How on earth, can Bhikkhu Sujato be considered a valid judge in this matter? What are his qualifications? I heard they were expelled monks from some tradition. If so, it is more suspectable.

@Blake Ven. Sujato may have been expelled from Ajahn Chah's monastery in Thailand due to his noble role in bhikkhuni ordination. But that casts no doubt on his credentials as a scholar and translator of the Pali Canon and Buddhism in general. Both he and Ajahn Brahm are validly ordained monks in the Tharavada Thai Forest Tradition, later expelled only due to political reasons and not due to parajika offenses. The Abhidhamma as a secondary source coming not from the Buddha himself, is explained by Venerables Bodhi and Analayo in this answer.

James Jenkins, those interested,
it's a sign of the Dhamma-Vinaya, the Buddhas teachings, to be very orthodox and it's because his good following disciples stayed by what was taught by him as much as they could remember and recollect, that his "(re)-legion" could be brought till this days and is still alive to be used.
What ever "unorthodox" approaches, often simply copies, are traced, can, for the most, be seen as not of what the Buddha taught and advice, yet he gave a lot of advice to proof such seriously without either to reject or take on it at first place, if unusual practices and teachings are approached and one of this sets of tools to prove is called Great Standards, also found under the link above, among other tools to verify the "orthodoxy" and validity of sayings and usual, mostly alien to the Theras (Elders of the monastic community).
While the practice of lay-followers may change over time, which is surely often also followed by certain disciples and particular communities of monks, of course always lead by certain improper desires, the ways the so called "Savaka Sangha" (community of good following disciples of Bhikkhus), the way of the Noble Ones didn't really changed, is still, even if hard to trace and find, alive although decaying naturally. Once the (Re)-legion goes astray, there is no much benefit for it, better it could not contribute much for benefit in the world, which is also a reason why this (re)legion would not adapt common desires simply for the sake of existing on or for maintaining ways of merely for the use of just livelihood and entertaining.
Once the "Religion" is or appears no more orthodox it will be no more maintaining a monastic Sangha which is a huge and unexcelled field of merits.
The essay and collection of That the True Dhamma Might Last a Long Time: Readings Selected by King Asoka may give also some impressions of the Dhamma-Vinayas ("Budddhisms") orthodoxy, which is actually, although claimed otherwise, even since the Mahaparinibbana of the Buddha, most compassionate this upholding of orthodoxy.

Now at that time, one Subhadda, who had renounced only in his old age, was seated in the assembly. And he addressed the bhikkhus, saying: "Enough, friends! Do not grieve, do not lament! We are well rid of that great ascetic. Too long, friends, have we been oppressed by his saying: 'This is fitting for you; that is not fitting for you.' Now we shall be able to do as we wish, and what we do not wish, that we shall not do."
But the Venerable Maha Kassapa addressed the bhikkhus, saying: "Enough friends! Do not grieve, do not lament! For has not the Blessed One declared that with all that is dear and beloved there must be change, separation, and severance? Of that which is born, come into being, compounded, and subject to decay, how can one say: 'May it not come to dissolution!'?"

What ever one nourishes, inwardly, outwardly, that will grow and resist for the individual as well as the opposite. It's seldom, very seldom that one gives into Upasnissaya of the Noble Ones, but having done and do so, one does not need to worry to come not near and sooner or later access the Orthodoxy that leads not only to heavens but to final release form all stress and suffering. Good and bad choices are individual ones, yours, which no one could force.
James Jenkins stated in his question: "It is of course impossible for the religion not to evolve at all as new questions and there answer have to addressed.", actually it is, was done by the Sublime Buddha, to release a timeless path and teaching, ever-trace and usable for those ready to be tamed.
(Note that this is not given for trade, exchange, stacks or entertainments binding one in this world but as means for an exit from this wheel)

There's no such thing as orthodox in Buddhism. But when translating the real meanings of Buddha is changed. And also in Pali canon it's mentioned that, buddha has mentioned dhamma should not be translated to Sanskrit, its believe that reason for saying that is tge true meaning of words are changed when translating. Eg: Lokaya = World (Loka Sutta), And when we add ‘a' infront, which is Aloka it means Light. So when you uproot Loka (world=Five Aggregates of Clinging) you will see the Aloka = Light which is Nivana or Enlightment.
So the meanings of these suttas are built in to words it self (This is Pali and Sinhalese language).
Apart from that ther's no any thing call orthodox.

translations are difficult even within english.  e.g. greed vs lust vs craving...clinging vs attachment...too much repetitive words

That's a broad question, I think the answer is "yes and no", so I'll try several small answers.

The word "Orthodox" has several meanings:

The true or correct teaching, the Right doctrine
By extension, and with reverence to the founder of the religion, the earliest or original doctrine
A conformist practice, a practitioner who tries to conform to the orthodoxy
A school or church which is named "orthodox"

Maybe everyone -- Buddhist or not -- wants to seek or have, or will claim to have, #1 ... even if their version may appear to contradict #2, #3, and/or #4.

According to Wikipedia, one of the current schools is called "Theravada" (the Way of the Elder Monks) which seems to me (though I may be wrong) to imply "original" or "orthodox".
It says the name derives from  "Sthavira" (which I find a bit strange because now there's bias against Sanskrit in favour of Pali, but that's a different topic).
This Origin implies that schools used to argue (and split) over who was orthodox and who was schismatic.

I've seen a modern user (on this site) write that this kind of topic is of interest to scholars and historians, but that "to us, it's just Buddhism".

What is in a name, anyway?
There are political parties named "Conservative" or "Socialist" or "Republican", but that's just the name.
There's little difference IMO between the Orthodox and Catholic churches -- mostly a different set of bishops and a distinct geography, i.e. Eastern versus Roman.
So with such large churches having such slight differences, and a schism which didn't happen until 1054 AD, you might feel safe in thinking that at least one of these churches is "orthodox". But then the protestant reformation happens -- people say, "The church is teaching and practising in ways which Jesus would never have agreed to".
And so you get people like John Fox who don't support the Established church but claim to be (and seen by some to be) closer to the truth (maybe closer to the "spirit" of the doctrine) than is taught from scriptures.
Perhaps there were already differences, between the "Buddhism" that was taught and practised when Gautama Buddha was teaching (in maybe 450 BCE), and "Buddhism" when it became the State religion in about 250 BCE.

Buddhist schools today (and historically) put some importance on "lineage" -- who taught your teacher (etc.)?
Many people will see that (i.e. a living teacher) as more important than the history-of-literature considerations
There's also sometimes a question of whether someone has been authorised (by their own teacher or school) to teach.
So that's a bit of both: i.e. traceable historically, and modern.

Everyone agrees that the Buddha's doctrine, the Buddha's words -- Buddhavacana -- are important and good.
So people sometimes disagree about whether something should rightly be considered or classified as "buddhavacana", and have different definitions.

The earliest Buddhism was pre-historic (by which I mean "oral history but not written") -- see for example Early Buddhism and Pre-sectarian Buddhism.
The official or canonical answer to that fact are that "Buddhist councils" were convened and they decided what's what, and we accept that.
Even so there are scholars and practitioners who think that on at least a few points it's likely that the current doctrine isn't or can't have been "original" (see this answer for one example).

Part of the monastic code is that you shouldn't cause a schism in the sangha (which I guess inclines toward orthodoxy).
There's some emphasis in the doctrine though about what "knowing for yourself to be true", so it's not maybe meant to be a slavish adherence to nonsense -- not "conformism above all else".

The above all seems quite pedantic. I think there are entire countries which get on  without bothering which such trifles -- for example:

Followers in Vietnam practice differing traditions without any problem or sense of contradiction. Few Vietnamese Buddhists would identify themselves as a particular kind of Buddhism, as a Christian might identify him or herself by a denomination, for example.
The overall doctrinal position of Vietnamese Buddhism is the inclusive system of Tiantai, with the higher metaphysics informed by the Huayan school (Vietnamese: Hoa Nghiêm); however, the orientation of Vietnamese Buddhism is syncretic without making such distinctions. Therefore, modern practice of Vietnamese Buddhism can be very eclectic, including elements from Thiền (Chan Buddhism), Thiên Thai (Tiantai), Tịnh độ Pure Land Buddhism, and popular practices from Vajrayana.

Perhaps there are some differences but they're not a big deal, not worth fussing about. Or maybe it can be said that the schools have a lot in common.

It may be that questions of "orthodoxy" are a type of conceit -- "I am orthodox, we are orthodox, you are not orthodox".
I say conceit because, to me, "orthodox" implies a comparison (i.e. compared with unorthodox or non-orthodox), and this answer implies that comparisons derive from conceit.
We are also warned that conceit and so on, maybe attachment to views, lead to sectarian arguments.

In practice I think that, for some people, their view of Buddhism overlaps with nationalism ("our country has the best, perhaps the most orthodox, form of Buddhism") or sense of national identity.
I guess that's human, as far as it goes, unless it becomes inhumane.

The vinaya (the monastic code) changes little or not at all. There's a story associated with one of the suttas, that at parinibbana the Buddha said he'd allow the monks to change any minor monastic rules, and they never did because they'd never agree on which rules were only "minor".
There are different versions of the vinaya from country to country, but that's an example of an orthodoxy.
In practice there are "monks" who don't try to follow the vinaya in detail.

I guess conformance is sometimes judged by an abbot and/or community of monasteries.
A monk who doesn't comply might be excluded from a "lineage" (e.g. here and here for an example).

What Lord Buddha Preached can be applied for the past present and future without changing a word or a letter. Lord Buddha never keep a space for us to add anything or delete anything or rewrite any context matching to the current scenarios.  Examples given in Buddhism well matched with all three periods.
But unfortunately in later stages with the different explanations few "Nikaya"[Associations] created among the monks. yet still the Pure Lord Buddha words still prevail with the Thripitaka.
People name them in different ways and some make them as their income sources.  Some name it orthodox buddhism,  some name it new aged buddhism, some name it Mindfulness Buddhism etc.
This is the Mirror buddha gave us to Identify Buddhism.
If any thing that remove kilesa [Defilement] — lobha (passion), dosa (aversion), Moha (delusion) in their various forms, which include such things as greed, malevolence, anger, rancor, hypocrisy, arrogance, envy, miserliness, dishonesty, boastfulness, obstinacy, violence, pride, conceit, intoxication, and complacency and instead improves kusala [Wholesome], skillful, good, meritorious. An action characterized by this moral quality (kusala-kamma) is bound to result (eventually) in happiness and a favorable outcome it is preached by buddha and should be followed.
Also You can apply them to

Raga Vinaya - Raga-vinaya Sutta[The Subduing of Passion]
Dosa vinaya - Pema Sutta-[Affection]
Moha Vinaya - Mula Sutta-[Roots]
Chathuraarya sathya - Four Noble Truths
Aaryaashthangika Magga - Noble Eight fold Path
Patichchasamuppadaya - Dependent origination
Moha Vinay Sutta is there in Sinhala and Pali but could not find in English Version.

What Lord buddha taught us if anything that matches to above one of the factors just accept and follow if not even some told that lord buddha preached just neglect it.
All these are purifying your mind or consciousness from the defilements and direct to Nibbana. If anything not fulfill the above path neglect them.
Read one's own mind - Sacitta Sutta: One's Own Mind
There are thousands of sutta to check whether you are in correct path.
May Triple Gem bless You.


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Does studying mathematics or science lead to a practitioner of Buddhism acquiring wrong philosophical views and mental afflictions?
Among the steps needed to attain enlightenment, a practitioner of Buddhism needs to abandon the wrong philosophical views that they acquired due to either wrong teaching or wrong study. In this sense, a practitioner that is less educated need only remove his or her sense of self or ego and the afflictions due to his or her present body. However, a practitioner that is educated would also have to remove the philosophical views acquired through wrong learning.
As paradigms in science have historically been replaced by new paradigms a la Kuhn, this means that science is necessarily a wrong view. For instance, a person living in Newton's time would have studied the absoluteness of time and space, but that view was displaced by Einstein's relativistic paradigm. Whatever science we are learning now, whether it be quantum physics or evolution or species, given the historical record, would be a wrong view and replaced by a more correct paradigm in the future.
Even mathematics have proven to be contradictory through history. At first, set theorists believed in unlimited comprehension till Russell's paradox showed the need for bounded comprehension, in the fateful saga of Russel and Whitehead's Principia Mathematica. Pythagoras's theorem was thought to be unconditionally true, but now it is true in only one of the three absolute geometries and physicists now believe our world to be non-Euclidean, in which Pythagoras's theorem fails.
After one is reborn in another world, the physics or mathematics of that world would likely be very different, and one's body would also likely be very different. This probably indicates the impermanent nature of the science and mathematics of our current society.
Are you also of the opinion that the learning mathematics and science causes a person to acquire wrong views? Would this lead one further away from enlightenment?

The 14th Dali Lama's education includes logic among many subjects, including science, and is "truly interested in participating in something substantial about science"

Science and mathematics are neutral. Scientists and mathematicians, on the other hand, are not. As a fellow mathematician, all I can say is that very deep down, in the core of science, there's faith; faith in the senses, faith in matter and faith in reason. Most materialistic scientists will hide or even be unaware of this fact, but it's there. As long as you don't forget this, you'll be fine. B. Alan Wallace wrote a fantastic article about this. You can read it here.

If you are looking for enlightenment you should be concerned of not being attached to these studies, or averse to what you disagree. The same fits to Buddhism itself, you should't become absorbed, or obsessed, to the Dharma.
All philosophies are mental phenomena, they aren't either good or bad in themselves. But they can hinder your search for enlightenment if you are too concerned about them.
Math and science share a side of problem elaboration and solving. So it would contradict Buddhism if you enjoy or think it is meaningful to be worried about all those problems. Over-thinking about anything and having a heavy attitude over theories or facts are opposite to the practice of meditation.
The point of meditation is to not being absorbed to mental elaborations. So there is no sense to think all over a sitting session. Then this extends to daily life, there is no sense to have a sharp and clear mind when meditating and daydream in the rest of the time.
For short, the point isn't what phenomena you engage, but it's how you engage to phenomena. If you can elaborate on any philosophy in a detached way it wouldn't be a problem at all. So the practice would be to think while being present and aware. (yes, this one is quite paradoxical)

I would like to point out that this is essentially a Hinayana view, and is not universally applicable to all Paths. Another view is that to be totally absorbed (completely un-distracted) by a topic of any kind is the same as concentration meditation, and has the same effect on mind. This means that enjoying doing problem solving is not contradictory to Buddhism, any more than enjoying your meal totally would be. Then, you are left with contemplative and spacious meditation to do separately.

Study of mathematics or science in and of itself is orthogonal to practice of Buddha-Dharma. But a side effect of study can often be a sense of pride based on the false conviction that one now knows everything there is to know about the way the world operates. This could be a serious barrier for entry into Buddhism and a source of misinterpretation of what Buddhism is actually about.

Mathematics, science, logic fall to the field of perception. If you conceptualize things and hold on to them as reality then this can be a hindrance.
You have to try to see things as they are without the clouding of perception.
Initially perceptions will be strong, but when perceptions arise you should try to be equanimous without clinging or reacting to the sensations associated with the perception and it's trigger. With this your perception weakens, and ultimately when you realize some form of sainthood, it ceases momentarily.

I don't agree with the spirit of your comment... everything we do or think falls to the field of perception, including the suttas, and everything else about "practicing" a path. We cannot be outside of perception as it is the only way to receive knowledge. The clouding of perception is not quite accurate either.. it is the clouding of the mind, believing that perception IS reality, that is the problem we are trying to solve. Perception cannot cloud the mind, the system of mind is prone to being clouded by WHAT we perceive as being real, which is what causes clouding.

If you are a Tantric Buddhist, you could use Mathematics and Science AS a path to enlightenment.
Also, the word 'wrong' is not relative to some 'right' which is known to Buddhists. The Eightfold path is a conjecture that "seems to work ok", but the Buddha himself said there were innumerable paths besides it.
So, this question could be answered in many ways, from many different viewpoints. It all depends on how you have decided to practice.
Buddhism is too large a viewpoint to answer this question.. you need to narrow it to what vehicle, and even flavor, of Buddhism as it is practiced in the world to get a meaningful answer.
EDIT: It seems that many here are pointing out that studying a difficult subject outside of Buddhism can lead to pride or distraction or attachment. I agree.
The broad point I am trying to make is that this is not any different than being prideful in anything, and does not in itself constitute a danger to your path, any more than being prideful in your appearance, strength, or taste in wine would be. In this way, there is no difference between Math and Literature, or between Physics and Dharma Studies. Thus, I maintain that there is no area of knowledge that will lead you to being more prone to pride, as long as you maintain your path while learning it.

I don't understand the first paragraph (which says that "a Tantric Buddhist could use Mathematics and Science as a path to enlightenment")? Could you add at least a little explanation of what Tantric Buddhism is, to clarify how it could use maths and science as a path, or to clarify what its path to enlightenment may be?

Well, the first thing is.. Enlightenment is Enlightenment. We can analogize that "one apple is very much like any other apple".
Secondly, Enlightenment comes in flavors, which are predicated by the path down which one walks. Every individual's attainment is different, and has a different flavor.
There are many different paths. The broad path called "Tantric" or "Vajrayana" is one which is interested in using all ordinary experience in the process of discovery. This includes learning Mathematics or Physics, and applying it to realization through contemplation.

The Right View of the Dhamma is only related to spiritual liberation i.e. the permanent cessation of suffering. Wrong Views are views that contradict Right View e.g. eternalism, annihilationism etc.
Science and mathematics are neither Wrong View nor Right View. They are simply worldly knowledge unrelated to spiritual liberation.
Lay people are taught to practise the Five Precepts and maintain livelihood in accordance with Right Livelihood for lay persons as taught in AN 5.177. In the sutta quote below, we see the Buddha praising the lay characteristic of being consummate in initiative, for mastering and practising worldly crafts. Lay persons need it for their livelihood.
So, science, mathematics and other worldly knowledge are not wrong view. But of course, any kind of exertion in worldly endeavors can lead one to strengthen their sensual cravings and cravings to become something.

[The Blessed One said:] "There are these four qualities, TigerPaw,
that lead to a lay person's happiness and well-being in this life.
Which four? Being consummate in initiative, being consummate in
vigilance, admirable friendship, and maintaining one's livelihood in
tune.
"And what does it mean to be consummate in initiative? There is the
case where a lay person, by whatever occupation he makes his living —
whether by farming or trading or cattle tending or archery or as a
king's man or by any other craft — is clever and untiring at it,
endowed with discrimination in its techniques, enough to arrange and
carry it out. This is called being consummate in initiative.
AN 8.54

The world is full of ideas. The ideas themselves do not cause wrong view. The solution is not ignorance. Opening one's mind to them, or education, is the opposite of ignorance. The Mind and Life Institute is a living example of doing so by one of Buddhism's most advanced practitioners -  the Dalai Lama.

To be short and to the point, no. It is my understanding that Pure Desire is the absolute teaching of Buddhism. So, as long as you don't get the feeling that you must due to the desire, you should still reach nirvana based on this issue.

Welcome to Buddhism SE. Maybe you could elaborate on the content of your post, i.e. what "Pure Desire" is and why one must not get that feeling. Thank you.

I think wrong learning is always problematic and likewise wrong convictions.
The scientific method of doing experiments for discovery & faĺsification is really a general modus of reasoning & acquisition of knowledge.
It is said that a mathematician's greatest weapon is proof by contradiction and to me he doesn't really care what it is he proves.
Mathematics to me is about putting aside one's delusion and just following wisdom.
Ie
At some point nobody knew how to count a negative multiplied by a negative and would speculate about it until someone actually set up an equation and saw the relations & the answer with intellect.
To me the Bodhisatta likewise developed wholesome lines of reasoning until these came together to paint a perfect picture of the elements & their conditional relations; he saw that 5 aggregates are not self, he saw that 4 aggregates have objects & are conjoined, he saw that the element which is called mind consciousness or intellect arises as one thing & ceases as another.
To me science isn't about views but rather truth & falsification of dumb ideas.
To me Buddhism was most impressive because i saw that the Buddha knew things which i've been told he weren't supposed to know, things that are recent scientific discovery & theory.
It is just very impressive because at that point him knowing these things is  basically a scientific miracle which a person trained in those disciplines can recognize as such.


text:
Is killing vermin and insects justifiable?
The first precept goes something similar to

I undertake the training rule to abstain from killing.

Now, I understand that, for instance, eating meat is allowed, but what about, for instance, killing vermin which might damage food or cause disease (such as mosquitos in places where malaria is common)?
Is killing justifiable then?

Just try to avoid situations where you might have to kill.

The beauty of the precepts is that they are impossible for ordinary human beings to fully observe.  The precept against killing is an example of this. My body's immune system kills all lifeforms that it doesn't recognize.  I step on and crush innumerable microorganisms.  But the first precept asks us to minimize the amount of harm we do in the world.  In the teachings of Thich Nhat Hanh, the precepts are trainings, not commandments.

But neither of those are something you're really choosing to do. It's impossible for you to not step on microorganisms, or the odd insect - but it's not the same as spraying insecticide to kill a whole nest of ants so they won't come into your kitchen.

I am very wary of either-or questions. There is usually a third way.  To keep rats out of my own kitchen, we have covered all possible ways for them to get in.  The rats still live outside, often in the high weeds of my backyard.  I try to keep the weeds low to discourage the rats and keep them out of danger.  The first precept is about harm reduction and love for all beings.  It goes beyond just killing.  The first precept asks us to avoid causing harm.

You nailed it- the precepts are trainings, not commandments.

I wouldn't say "that's the beauty of the precepts," that they're impossible. You don't undertake the precept to avoid something thinking in the back of your mind "this is really impossible." I think going down this route of thinking is a mistake.

@Wideshanks: "The Diamond Sutra teaches us that it is impossible to distinguish between sentient and non-sentient beings...The First Precept is the practice of protecting all lives, including the lives of minerals." -- Thich Nhat Hanh
We must eat, therefore we must, at some level, kill, be it animals, plants or minerals.

Ah. I think it'll be better to prefix that somehow, maybe with "From the Thich Nhat Hanh/Diamond Sutra point of view...", because you're going to very quickly run into others with much different views about the observance of precepts.

Perhaps one can say that the beauty of the precepts is that there are deeper, more subtle and more extensive ways in which one can practice them. As we train with this precepts, our understanding increases which leads to a more nuanced and extensive practice of these precepts.

I do not agree with this answer, the Karma is created with intention, therefore killing an insect you couldn't see is not a break of the precept. There is a story in the dhammapasa about it regarding a blind monk stepping in insects.

P.S. The problem with a site like this is that while it remains written / read in English, it's bound to have a Western focus and thus Western dilutions to the original beliefs. And answers like this will be accepted because it is easier for the Western OP to accept this.

I've never studied Buddhism in depth but I came here because I found myself not agreeing with my own action of killing gnats in my house with an electric fly swatter. I assign a high probability to karma being a real thing. I do feel like this answer was accepted out of convenience having read the others; however, how else am I going to get rid of these damn gnats? I can't catch them all.

In a previous life the Buddha is said to have killed a human being, knowing full-well the potential danger to himself. He did it to save others. This story is presumably preserved for a reason, It teaches that an ethical rule cannot work in all situations. The rule would be to apply the rule as appropriate to the situation. The same problem arises from Kant's Imperative but it may easily be solved in the same way.

In order to understand this issue, we have to understand morality according to Buddhism. In Theravada Buddhism, morality is completely based on the effect that an act has on the mind of the actor. Hence, eating meat need not be karmically negative, yet killing Hitler to "save" others from suffering need be, since it requires defilement to take the life of another.
It is not considered immoral to do something just because it has negative consequences for others, nor does a positive effect for others constitute a sufficient condition for morality.
The reason for all this is that Buddhist morality is defined by its potential to lead to focus/concentration and eventually wisdom. One eats meat, knowing that the act is harmless, and so one's mind remains calm and the nourishment supports meditation practice.
The reasons behind killing our less evolved brothers and sisters - insects, spiders, foxes, etc., are inconsequential. Even if killing a single mosquito would end all cases of malaria in the world for ever, the (Theravada) Buddhist philosophy would be to abstain from killing the mosquito. Acting to prevent suffering can actually considered to be an unwholesome act, since it generally requires aversion to said suffering. In (Theravada) Buddhism, we act to prevent unwholesomeness, not suffering, since suffering does not lead to suffering, but unwholesomeness always leads to suffering.

The five precepts are an absolute entry-level teaching that is designed to help the practitioner master basic discipline of self-control and self-reflection.
Abstaining from killing, stealing etc. implies basic ability to watch one's mind for harmful thoughts and emotions, and to prevent them from getting acted out.
In light of the above, the no-killing rule should not be understood literally, as an absolute law, but as a guideline for training the mind. It is not acceptable to hurt or harm any creature (big or small) out of anger, out of competitiveness, or out of ignorance. This is what this rule is about.

It's not justifiable even if the killing is for self or others protection.
If killing of an animal fulfills below five conditions it will give bad results (akusla karma vipaka)

There should be a living being
Knowing that its a living being
Intention of killing
Act to kill
Animal is killed by the act

Note:
Even If someone kills an animal which is suffering from unbearable pain (like with an injury), with the intention of releasing it from the pain. It will give Akusala Karma vipaka.

Do you have source information on this?

@Adamokkha Yes, but it is in Sinhala (I live in Sri Lanka), But I will try to find some source on the web...

First rule (of layperson) is actually includes intentional killing of any animals down to even insects. See for reference http://www.accesstoinsight.org/lib/authors/bodhi/wheel282.html#prec2

"I undertake the training rule to abstain from taking life." Here the
  word pana, meaning that which breathes, denotes any living being that
  has breath and consciousness. It includes animals and insects as well
  as men, but does not include plants as they have only life but not
  breath or consciousness. The word "living being" is a conventional
  term, an expression of common usage, signifying in the strict
  philosophical sense the life faculty (jivitindriya).

But you will not be expunged from being buddhist if you violate that, you just stain karma, accumulate demerit, and lose protection.

I feel like sometimes the "plain", most obvious meaning of the rule (e.g. don't kill people) is taken to extremes (e.g. killing mosquitoes that spread diseases which kill you, killing a bear which is eating you), and the very intuitive repulsion the mind feels regarding the extreme is used to sow doubt in the rule itself.
I don't think the Buddha taught by going to extremes like this. How about start off by not killing people, for any reason. This, at least, is pretty straightforward, how the hate and lack of compassion required for killing people is damaging to you.
Next, examine the ways in which you'll sometimes casually kill insects and set it within the context of kamma and rebirth. Does it seem unskillful? If it does, then abandon it. Next, examine how you'd feel if something were trying to kill you. Do these actions of your mind reacting against the assailant seem unskillful? If they do, then abandon it.
Think of it like taking your mind to progressively more subtle forms of self-examination to abandon more and more forms of unskillful behavior.
The way of thinking in the original post is more like taking the prohibition on killing to an extreme and then allowing the mind's repulsion against the extreme case to take over and turn you against the precept.
But the mind that hasn't gone beyond suffering is the problem. You have to be careful how you let it make decisions about these things.
There are instances where the Buddha says a question should be answered with a yes/no response and others where the answer should be qualified by re-defining the question.
http://obo.genaud.net/dhamma-vinaya/ati/an/04_fours/an04.042.than.ati.htm

First the categorical answer,
  then the qualified,
  third, the type to be counter-questioned,
  and fourth, the one to be set aside.
  Any monk who knows which is which,
      in line with the Dhamma,
  is said to be skilled
  in the four types of questions:
      hard to overcome, hard to beat,
      profound, hard to defeat.
  He knows what's worthwhile
      and what's not,
  proficient in (recognizing) both,
  he rejects the worthless,
      grasps the worthwhile.
  He's called one who has broken through
      to what's worthwhile,
         prudent,
      wise.

I stopped killing mosquitoes long time ago and started using nets and mosquito repellent lotion. You really don't have to kill them.

This answer does not really get at the key issue - is it justifiable to kill insects? Certainly it is something we should try to avoid, but is it ever okay to kill an insect?

I think it might be a malformed question then. I can justify any behavior. If the question is "is killing every 'good karma,'" the answer is categorically no. Justifiable amounts to imagination.

@DespreTine Is that so? I am no expert, but surely there are some acts that are justified by Buddhist doctrine and other acts that are not. If it is genuinely the case that any act can be justified by Buddhist doctrine, then the question is indeed malformed, but I doubt that is the case.

Sect differences will matter a lot more here. Are we strictly adhering to Theravada orthodoxy? You could justify killing by making reference to the Jataka tales (bodhisattva kills a would-be thief/murderer to prevent them from killing others).

Yes, intentional killing is always bad Karma, whether you want to justify it or not.

In fact, justifying the killing can make the Karma worse as you also add ignorance into the mix.

As a practicing Buddhist, I would say, no, it is not.  Part of the problem is that great thought has been put into methods of killing, but relatively little thought has been put into alternatives to killing.  When I find mice in my house, I drive them to the park.
I have heard that there is some investigation into breeding mosquitoes that pass on a gene that makes their progeny sterile, or something like that.  Thus killing can be avoided in that situation.

Killing is never justifiable.
He cares not to step on an ant while walking, but did once while not paying attention. He walked on and he has learnt.
She likes the rose and plucks it and get stung by the thorns. She doesn't afterward try to get a tool to cut it to prevent another cut or step on it as retaliation. She looks, instead.
"such as mosquitos in places where malaria is common"
would be the same as someone who cusses at you for no reason, makes you angry, a cause arises in the sense, which in turns justifies your retaliation ad urges you to do it.
In the arising of cause in the sense, it draws a line for you "right" and "wrong", "good" or "bad", "kind" and "evil", put your feeling in one of them, urges you to counter the opposite of the other.

In Buddhism one of the main teaching is that any action as repercussions. Generally people do not like getting wounded, loosing a limb or body parts, dyeing, etc. When you do bad Karma the results you reap are similarly horrible as your action. So what you do to the insect will likely befall you in some point of your existence in Samsara.
Since this action in not to ones own benefit or the benefit or other hence is it unjustifiable. What is justifiable is what beneficial to ones self and others.
NB: In Buddhism the law of Karma is not absolute, but balance of probability interacting with the other Karma and Niyamas.
Also see the following which analyse the results of Karma. Generally what is not conducive to oneself or the others is not justifiable:

Cula Kamma Vibhanga
Brahmavihara Subha
Ananda Subha
Maha Kamma Vibhanga