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How do we sense the flow of time?
According to the Abhidhamma, at each given instant there is a consciousness that arises and ceases completely before the next consciousness arises. Each consciousness is only aware of the present moment (just an instant and only that instant) and therefore cannot know about previous instants.
So, how is it possible that we have a sense of the flow of time? How do we know that there was a past?

What arises every moment is the ego, not the consciousness. The consciousness always exists and is everywhere and always, so it is all that exists. The teachings of https://en.wikipedia.org/wiki/Ramana_Maharshi emphasise on this.

If that's an answer please post it as an answer, not post it as a comment. And the OP was asking about the Abhidhamma -- referencing a Hindu teaching isn't on-topic.

Past is a conceptual construct that only seems solid in the absence of careful examination. But if you look closely you will see that Past is assembled by the mind from multiple cues (as is Present by the way).
The experience of second-to-second flow of time is a byproduct of chitta-vrtti, the associative cycle, when each subsequent dharma (~thought) comes by association with the previous one. The sense of relatedness of the two dharmas is what creates the illusion of flow.
Disclaimer: this answer represents my own experience and understanding and is not meant to reflect an official position or to be consistent with views of any Buddhist school.

note that the question, whether past and future really exist, and how, was the reason for one of the early schisms in buddhism. Thus the Sarvāstivādin - "omniexistencialist" or "those who say that everything is", which is one of the orders whose canonic writings (in Sanskrit) are partly preserved are called thus  because they held, that past, present, and future all exist simultaneously now.

Thanks a lot for your answer, though there seems to be a difficulty in your explanation: how can a thought have any association with the previous one if there is no awareness of the previous one because the previous one already ceased without remainder?

@czamora Chitta holds one dharma at a time. Because dharmas never coexist in chitta at the same time, they can't interact with each other. The reflexive mechanism that creates second dharma on the basis of the first relies on associative memory to find samskaras (memory imprints) that are in some way "similar" to the first dharma.

@Zvolkov Where can I find this "associative memory" you speak of? Sounds like a concept from psychology, nor from ultimate reality.

Buddhist psychology was largely based on Hindu psychology of their time. From my research of various Buddhist and non-Buddhist sources like the various commentaries to Patanjali's Yoga Sutra, I came to this interpretation of citta-vritti as an ancient description of the association cycle. Of course they never called it that.

Space (Akasa Pannattis) and time (Kala Pannattis) are a conceptual or perception based construct (Pannattis). Since the notion of time is a perpetual construct this is not what is called an Ultimate Truth. The passage of time is perceived by an observer thought his experience of the "world". We perceive a difference on when one experience happened vs another.
See: Time and space: The Abhidhamma perspective, Professor K. N. Jayatilleke Memorial Lecture 2003 by Y. Karunadasa.. Also The Dhamma Theory by Y. Karunadasa which discusses Pannattis.

But the question remains, how do you perceive a difference on when one experience happened vs another when you only have consciousness of one of them (the present one) and know nothing about any past experiences? [In fact your answer begs the question, because if you can perceive a difference on when something happened then you already have a sense of time]

You perceive I did this for lunch and that for breakfast and perceive that breakfast was before lunch. If you see something falling you perceive it was at a higher elevation before than after. What you are doing something interesting you perceive time flows fast while you perceive time flows slowly when doing boring things.

So, how is it possible that we have a sense of the flow of time? How do we know that there was a past?

According to my experience (not according to doctrine), I have a sense of time in the following ways:

Sometimes (i.e. at some present moments) I am imperfectly remembering something from the past (a feeling, a person, a place); i.e. I'm presently conscious of a memory or imprint
Sometimes (i.e. at some present moments) I am planning (trying to foresee) a future action or experience, e.g. "I will plan to change my regular routine in order to go to a lesson next Thursday evening because I want to repeat a previous/learned experience i.e. that I successfully went to a previous lesson on the previous Thursday"
I label time (a clock for the time of day, a calendar for the day of week) and therefore notice that the 'current time' changes; for example I'm writing this in the day-time, but as I was writing it the thought occurred to me "although it is visibly day-time now (I see day-light) there is such a thing as night-time, when it's dark and when in the past I was outside and saw the nighttime sky with stars and moon"
Sometimes I see things which are in motion (e.g. a person walking or a plant blowing in the wind); my sense of sight is trained to perceive motion; and my mind has been trained to associate motion with time (a change in location over time)

The motion of objects (something which was in one location and is now in another location), and counting period cycles (e.g. planet's orbit, the motion of a pendulum, the ability to count ocean waves on the shore, or to count breaths, or to count foot-steps) is I think more-or-less the definition of 'time'.

The time flowing is a purely a mental projection.But how?
Imagine yourself in a field,
here
you do not have a watch
it is dark sun is not coming up
can you guess the time now?
This is an actual experiment to explain how humans experience time.Time for humans  is very easy to understand,
watch a movie for 2 hours and sit down,start meditating for 2 hours.You will feel like it is 4-5 or 5 1/2 hours.
The experiencing of the flow of time is relative to what you are experiencing now.If what you are doing is exiting time is faster to your mind (Like a date with the love of your life).
But if what you are doing is boring time is slower to your mind (Like school)
So the conclusion is the feeling of time passing by is a complete illusion of mind thinking.If the mind was asleep like you do in the night you will not feel it at all.
(If there was no clock in your house can you say how many hours you slept last night?)

So what about the Past?
Past is not a real thing.Your brain can't even fully memorize a single event.What it does for this amazing magic to happen is very simple.
It is more like how you studied back in the school.
Your brain/mind remember the most important events of a memory and fill in the blanks to make the rest of the memory.But you can't find a difference between the memory and the real event.Because what your mind makes up is all you can remember.
For example try to remember the last time you went to see your grandmother.
Can you remember what shoes you were wearing?
Can you remember who you met before going there that day?
I guess you will not be able to.Brain did not recorded those things in the permanent memory.Because none of those small things were important to make the memory in the first place.


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Are there formal mechanisms in any Buddhist institutions that explicitly reconcile Buddhist principles with science?

If science proves some belief of Buddhism wrong, then Buddhism will have to change. In my view, science and Buddhism share a search for the truth and for understanding reality. By learning from science about aspects of reality where its understanding may be more advanced, I believe that Buddhism enriches its own worldview.
  -- Tenzin Gyatso, the 14th Dalai Lama in "Our Faith in Science", The New York Times

This is all very well, but are there formal mechanisms in any Buddhist institutions that explicitly allow Buddhist principles to be reconciled with the findings of science?

Not sure I can answer the question, but I am trying to understand what you're asking. Do you mean is there a similar "papal bull" mechanism to change fundamental beliefs of the religion?

It would help if you'd specify which kind of Buddhism you have in mind. Only an institution can have a formal mechanism. This implies you have some institution in mind (maybe FTMT or the Tibetan Government in exile?) Buddhism as a whole has a lot of institutions and even people like myself who go out of their way to not participate in an institution.

@matthewmartin, any kind will do.  :-)

The general claim in Buddhism, or at least in Theravada Buddhism, is that a Buddha is omniscient. That makes it difficult to question what the texts claim the Buddha himself said. In a couple of places this seems to put science and Buddhism at odds (e.g. causes of earthquakes).
The closest we have to what you are suggesting is an act of the sangha; after the Buddha passed away, we have record of a Buddhist council where they discussed whether to revoke the minor monastic rules as the Buddha had allowed them to do, and they decided as a group not to. Later sangha councils edited the canonical texts but would never have redacted something that they thought the Buddha had said in error.
I think, at the very least, unlike faith-based religions, Buddhism doesn't rely on absolute statements of truth, but rather practices that lead to self-realization; so it doesn't matter as much if statements in the canon like the causes of earthquakes and the size of the universe, etc., are accurate. What matters is if the path leads to the goal, and that is to be verified by oneself.
As a result, you find more marginalizing of problematic teachings, rather than striking them out. First of all, because the Buddha was said to be infallible, but second of all because we know that we are not. The fear of wrongly striking a teaching out of ignorance is too great. But, we can always ignore troubling passages, I guess similar to how Jewish people ignore Leviticus for the most part.
So, no, there isn't really such a mechanism, afaics.

The goal of science is most complete and accurate description of the world. The goal of Buddhism is to clearly realize relationship between mind and experienced reality and to transcend the limits of any single description of the world. So in a way, Buddhism lives in an infinity of higher order than the one science lives in. If anything, it is science that should reconcile with Buddha-Dharma, by becoming aware of inherent Emptiness of all views, not the other way around :)

That is what I would characterize as an act of faith.  Faith and science are oil and water. :-)

Just to make sure I understand what you mean, may I ask what exactly you would characterize as an act of faith?

"It is science that should reconcile..."

The notion of some assumed conflict between science and Buddhism comes from misunderstanding of Buddhism. Once you clearly see Buddhism's ground, path, and fruition, you will clearly see that Buddhism and science are not in conflict. I would go as far as to say that any scientist worth his/her salt is already a buddhist in effect (minus the raft).

Arguably science has no need to change, simply because science is already aware of "the inherent emptiness of all views" : a scientific theory arises, is modified, and may eventually cease, in dependence on causes and conditions such as experimental results that support, modify or contradict it. That's how the scientific method works.

@BrianDrummond correct, at its best, science is already Buddhism, scientific view is enlightened view. In practice however, not all scientists consistently apply Emptiness all the time, as is evident from the way they posit and argue their theories.

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What is the role of relics in Buddhism?
I recently learned about an episode of Chinese history when relics associated to the Buddha were relocated to China and Han Yu writes to the Chinese Emperor in a text titled "Memorial Discussing the Buddha's Bone" (PDF), expressing his disagreement with the Emperor's decision to pay his respects to the relics.
I don't quite understand the significance of this event, because I don't understand the role or significance of relics in Buddhism.
What was the role or significance of relics for 9th century Chinese Buddhists and what role do relics play in contemporary Buddhism?

After The Buddha's death, his ashes are said to have been divided into eight portions. Source:Wikipedia

The cause of arising of the Buddha’s relics was from the desire of our Lord Buddha before his Parinibbāna (the Great Decease of the Buddha).
Normally, the Buddha who lived a long life to settle the Buddhist Legend, had his own relics in a piece of natural golden bar, which could not be shared among the people in their Buddha period and could not be placed anywhere. Hence the construction of the Buddhist sanctuary was required to be done in one place only. Our present Lord Buddha (Sakyamuni Buddha) considered that his teaching period was only 45 years which he thought not too much compared with the previous Buddhas. He also thought that his instructions were not expanded enough and taught to those who were not yet born on time in his legend. Anyone who received his relics for respecting would get a lot of Puñña (the accumulation of good blessing, fortune or well-being) so he wished that his relics be scattered to all directions except 7 pieces (1 frontal bone, 4 teeth and 2 collarbones).
All of the above mentioned information was presented identically such as in the Sumaṅgalavilāsinī, Paṭhama Sambodhi Kathā by the Supreme Patriarch Kromphra Paramānujitajinorasa, Mulasāsanā Scripture, Jinakalamalipakaranam by Ven. Ratanapañña Thera and Phrachaolieplok Scripture.

Source:The history of the arising of Buddha’s relics
If you want to know more depth details, Please read Maha-parinibbana Sutta: Last Days of the Buddha

Eight portions there were of the relics of him, The All-Seeing One, the greatest of men. Seven in Jambudipa are honored, and one In Ramagama, by kings of the Naga race. One tooth is honored in the Tavatimsa heaven, One in the realm of Kalinga, and one by the Naga kings. Through their brightness this bountiful earth With its most excellent gifts is endowed; For thus the relics of the All-Seeing One are best honored By those who are worthy of honor — by gods and Nagas And lords of men, yea, by the highest of mankind. Pay homage with clasped hands! For hard indeed it is Through hundreds of ages to meet with an All-Enlightened One!

Good answer, except the OP was asking about significance to 9th century Chinese and modern times; this doesn't really address that.

I'm less interested in the relics than in the significance of the relics for Buddhists. The sources you provide say very little about this.

I cannot answer for "9th century China" specifically, but in the Lotus Sutra it is clearly evident that the only Buddha relic is the Dharma itself. The Lotus Sutra and other Mahayana texts are the Buddha relic. Within those texts are the real bones of the Buddha. Each character of the Sutra is a bone of the true Buddha-body. If one clings to Buddha's bodily form, one can never see Buddha's true form (Dharmakaya).
The teacher of the Dharma, chapter 10
(scripture 53)
"You need not enshrine my relics"

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Are Vajrayana and Tibetan Buddhism the same thing?
This is a hugely amateurish question, for which I apologize, but: are Vajrayana and Tibetan Buddhism the same thing? If not, how are they related?
In particular, does the term "Tibetan Buddhism" refer to a specific school of Buddhist thought and practice, or does it just generically refer to any sort of Buddhism that is practiced in Tibet?
Wikipedia treats the two as separate entities, but some other sources (e.g. this) treat them as effectively the same.

I would not say that the source you quote treats them as "essentially the same". Instead, it has, > It rather quickly spread out of India and became established in several parts of the Buddhist world, particularly in Tibet, where it became the dominant form of Buddhism. Indeed, the Vajrayana is often referred to simply as "Tibetan Buddhism." I read it as meaning that neither all Tibetan Buddhism is Vajrayana, not that all Vajrayana is Tibetan - only that they get mixed up in popular terminology.

No they are not the same, Tibetan Buddhism is a broader concept that subsumes Tibetan Vajrayana. Also, there's non-Tibetan Vajrayana, some still practiced in e.g. Japan.
To some degree all schools of Tibetan Buddhism, and particularly Karma Kagyu, recognize three yanas (Hinayana, Mahayana and Vajrayana) as subsequent stages on an individual's path to complete enlightenment. These days many teachers tend to have their student jump straight into tantra right after Ngondro (preliminary stage of Vajrayana training), but traditionally, the student is supposed to master the foundational theory, discipline, and meditation of Hinayana before proceeding to Mahayana, then master Mahayana's practice of subverting one's ego, and attain realization of nonconceptual emptiness, and only then proceed to tantric practices of working with Yidams (generation/completion), the Vajrayana proper.

so, do you suppose that esoteric buddhism does not exist outside tibetan buddhism? what do you make of shingon? shingon still exists, right?

Ah, you are right.

eosteric buddhism does exist outside tibet! i think...

Yeah, I know. Fixed the answer.

Vajrayana was practiced in China, Vietnam and Korea. This is often called esoteric Buddhism.
Kukyo brought esoteric Buddhist to Japan and founded the Shingon sect.
In Russia (well, Kalmykia and Buryatia now) Buddhism was essentially Mongolian Buddhism, which in turn came from Tibet.
And in the US, we have modern formulations of Vajrayana like Shambhala.
I think it would be more accurate to say that these are all forms of Vajrayana rather than forms of Tibetan Buddhism.  However, Tibetan Buddhism certain has the most mindshare, the most widespread institutional bases (monestaries and centers established all over the place), so Tibetan Buddhism is the elephant in the room when it comes Vajrayana.

Tibetan Buddhism is not all there is to esoteric Buddhism. There is also Shingon, which I know almost nothing of, except that it exists in Japan. Here is a wikipedia article, which I quote from and added some bold to

Today, there are very few books on Shingon in the West and until the
  1940s, not a single book on Shingon had ever been published anywhere
  in the world, not even in Japan. Since this lineage was brought over
  to Japan from Tang China over 1100 years ago, its doctrines have
  always been closely guarded secrets, passed down orally through an
  initiatic chain and never written down. Throughout the centuries,
  except for the initiated, most of the Japanese common folk knew little
  of its secretive doctrines and of the monks of this "Mantra School"
  except that besides performing the usual priestly duties of prayers,
  blessings and funeral rites for the public, they practiced only Mikkyō
  "secret teachings", in stark contrast to all other Buddhist schools,
  and were called upon to perform mystical rituals that were supposedly
  able to summon rain, improve harvests, exorcise demons, avert natural
  disasters, heal the sick and protect the state. The most powerful ones
  were thought to be able to render entire armies useless.
Even though Tendai also incorporates esoteric teachings in its
  doctrines, it is still essentially an exoteric Mahayana school. Some
  exoteric texts are venerated and studied in Shingon as they are the
  foundation of Mahayana philosophy but the core teachings and texts of
  Shingon are purely esoteric. From the lack of written material,
  inaccessibility of its teachings to non-initiates, language barriers
  and the difficulty of finding qualified teachers outside Japan,
  Shingon is in all likelihood the most secretive and least understood
  school of Buddhism in the world.

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Buddhism, mothers and earthworms
My first exposure to Buddhism was watching Seven Years in Tibet in my German childhood. Most memorable were the following two scenes of Buddhist monks in orange robes.
In the one scene, some monks were carefully making a large picture out of coloured sand in a room with large windows. Upon completion (after one year of labour), the monks would simply open the window to let the wind carry the picture away.
In the other scene, monks were very carefully turning soil. Apparently the monks had to be especially careful not to harm any earthworms, because, according to their belief, their mothers would be reincarnated as earthworms.
Needless to say, I found it very arbitrary at best that mothers should be reincarnated as earthworms and was troubled by this first impressions for the next decade or so. Unfortunately, I still haven't been able to solve this mystery.
So my question is, as it has been for many years, is there any connection between mothers and earthworms in Buddhism?

Not an expert here, but perhaps we should use [non-violence] as a tag rather than [ahimsa]? My understanding is that [ahimsa] is more a Hindu/Jain thing.

@senshin Right. I checked Ahimsa on Wikipedia, where it says "Ahimsa is one of the cardinal virtues and an important tenet of major Indian religions (Buddhism, Hinduism, and Jainism)". I'm fine with [non-violence], if that's the better jargon.

ahimsa is a Buddhist concept as well, but probably better to use the English, no?

@Yuttadhammo I think that we have both non-harming and non-violence in English. I opened a meta discussion.

The explanation quoted in the movie is, "Please, no more hurting worms. In a past life this innocent worm could have been your mother." Also it wasn't monks who were digging: it was Tibetan labourers.

I'm pretty sure the belief is not that earthworms become mothers, it's that every earthworm has most likely been your mother at some point in the past, as per the mata sutta (SN 15.14-19):

At Savatthi. There the Blessed One said: "From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on. A being who has not been your mother at one time in the past is not easy to find... A being who has not been your father... your brother... your sister... your son... your daughter at one time in the past is not easy to find.
"Why is that? From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on. Long have you thus experienced stress, experienced pain, experienced loss, swelling the cemeteries — enough to become disenchanted with all fabricated things, enough to become dispassionate, enough to be released."

So, the point is that the love and care we have for our mothers should really extend to all beings, since we are all intimately related - a corollary is that your boy/girlfriend has also probably been both your mother and your father at one point :)

"a corollary is that your boy/girlfriend has also probably been both your mother and your father at one point" And as a second corollary, my intestinal parasite at some point as well. Thank you very much for the reference.

@Earthliŋ If one of the answers looks good, would you be willing to accept it or supply feedback?

This question assumes frame of reference different from the one Buddhism operates in. The point of teachings is to produce a certain state of mind, that will affect your behavior in certain way, that will eventually lead to better results, up to and including Enlightenment for you and the rest of the sentient beings.
In this case, the image of mother is used as an epitome of unconditional love. By visualizing your mother and generating the feeling of love to her, you generate a certain emotion. Then, you learn to project this emotion on other sentient beings. In actual practice you start with the people who are naturally close to you, like your friends and relatives, and slowly expand it until all beings are included. The movie uses the worms scene to vividly illustrate to the audience the sheer depth that Buddhist compassion/love goes to.
Worms are not your mothers :) Everything is your mother. Everything is sacred. Everything is love!


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What is the starting of Samsara?
Every Buddhism believe in Eternity or Samsara. So, how can I imagine of Samsara?. What is the starting of it ?
 Any suggestions would be really appreciated.

It is unclear what you are asking. What is the "starting life of eternity"? Please clarify what exactly what you're asking about, so as to ensure that your question is not closed.

no need to be mean. English is a difficult language. This question should be written "Every Buddhist believes in eternity. So, how can I remember my first life?" edit: i have proposed it as an edit to the question.

@qweilun Is that what OP's question actually is? I'm not trying to be an ass; I just literally did not understand what he meant.

Sorry if I interpreted that way. That's what I think OP means. It's difficult to imagine OP would mean anything else. :)

It's a bit unclear. Do you want to know about your first life, like what you did, where you lived, etc., or about the first starting point of any being in his infinite times of material existence?

Is there a starting point to a circle? Just like that, there's no starting life to Sansara. But you can break this circle at 2 points.

Ignorance.
Craving.

That is when you attain Nibbana.

Yes , Eternity mean absolutely for Sansara. Fine . I would like to know what is the starting of Sansara ?

What is the starting of a circle?

if you asked about circle , that may be drawer . if you asked about an egg ,that may be han. So , everythings has their being. where they come from ?

but I don't mean that was due to Creator or God. I know Buddha didn't told about the starting of Sansara. Chritians has their starting life .They believe about Creator.

So what came 1st? Egg or the hen? This is a problem with linear thinking. You can touch any point of the circle and take it as the starting point. But there's always a point before it.

you gave me Egg or the hen for instance. pls give me an example for Sansara. Can you ? That is the point I would like to get suggestions.

Circle is the example

@SankhaKulathantille This is an interesting metaphor, but could you maybe be a bit more explicit? e.g. what exactly does "breaking the circle" mean? Does it mean something like "freeing oneself of ignorance"?

Yes, once you eliminate ignorance, you no longer crave. Therefore no clinging. Which means no rebirth. Read about Paticca Samuppada.
https://www.youtube.com/watch?v=n_llBSCXt6c

@Cataclysm Well, I don't mean to beat my own drum, but the question of origin had troubled me a lot. After years of practice and search I realized the answer to be Nothing. That is my theory. Everything indeed runs in a cycle. If you are really looking for an answer then you might want to check my solution of this problem at http://shunyavada.com/

According to the suttas, samsara has no beginning. There are many references to this.

The suttas you referenced don't say "no beginning": they say "inconstruable" and "not evident". Whether "the world is infinite" is one of the "unanswered questions".

The answer to your question depends on how one understands the word "start." Etymologically, the English word means to jump, leap up, or move or spring suddenly, thus, to arise, to come into being. In accordance with the law of karma, the whole process of samsara itself must be self-starting.
This can be proved logically based on the law of karma, which requires that every cause have an effect and every effect a cause. Since samsara is time itself, the essence of time is the identity of cause and effect, thus, the moment, which is then extended in space as past and future to create the infinitely differentiated  world that we experience.
However, as the illusory negation of reality samsara must inhere in the non-illusory, which is reality itself. Therefore, samsara also inheres in reality, and in that sense has a logical - but not a temporal - "origin." This "start" is the principle of karma itself, which is the inherent kinetic principle in transdual reality.
This is necessary to explain our experience of samsara. Otherwise, there would just be nothing at all. This point of identity of samsara and reality is, once again, the moment. Therefore, the answer to your question is that the start of samsara is the inherently timeless and therefore eternal moment, which paradoxically is the origin of time, space, and causality that endlessly differentiates in infinitely variegated patterns. This view of the cosmos remarkably presages certain theories in modern physics, especially the holographic theory of the universe.

Beginning of Samsara is stated by Buddha as not knowable for ordinary beings. Knowing rightly would be to not imagine in regard of its beginning.
Usually Samsara is imagined as round of re-births in the six realms, or much more detailed view as bhavacakra.

Your question has two parts so i will answer in the following order...
How to understand "Samsara" and how it works.
Sansara or Samsara is the word Lord Buddha picked to name a certain circle of death and life.
What is samsara
As we Buddhists believe as long as a being lust for existence he will be born according to his Karma.To this process we call "Sansara or Samsara".
So where is the start of samsara?
Even Lord Buddha was intrigued by the question and started to find a solution.The only way to do it is to look back into your own past to find your first life.So Lord Buddha went back countless amount of lives and understood that the "Beginning" is very ancient the time we have in a life is not enough to look back and see that life.So lord Buddha said this to the Sangha  "There is no point in looking for a start,it is too old and trying to find an answer is a waste of time".And advised that no one should try to find an answer to it (Because they will not be able to find it)
So my friend that question can't be answered by any being in the universe,Because if there is something out of Lord Buddha's reach it is out of anyone's reach.
So how does samsara work?
How it works is complicated but i will give you a simplified version of it.
Samsara needs fuel like your car,As long as you give fuel to it it will keep working and you will have life after life to live.
Let me give an example from lord Buddha....
"Karma is the paddy field,Lusting is the water,vinyana is the seed"
In the real world without water a seed will not grow,likewise without "Greed or lust" you will not be born,without it there is no samsara but as long as you have it you will have samsara and you will have to suffer in whatever karma brings you.

The beginning of samsara is inconstruable and not evident, yes, but it definitely happened when the mind-body phenomena emerged out of ignorance and started craving and clinging.

As he was sitting there he said to the Blessed One: "'A being,' lord.
'A being,' it's said. To what extent is one said to be 'a being'?"
"Any desire, passion, delight, or craving for form, Radha: when one is
caught up there, tied up there, one is said to be 'a being.'
"Any desire, passion, delight, or craving for feeling... perception...
fabrications...
"Any desire, passion, delight, or craving for consciousness, Radha:
when one is caught up there, tied up there, one is said to be 'a
being.'
SN 23.2

From objective perspective, Samsara is a beginningless round of deaths and rebirths the beings are stuck in. "Beginningless" means it has no beginning. The question you may ask: if Samsara has no beginning, and I am in it, how did I come to exist? This seems like a real puzzle.
Another piece of the puzzle is Buddha's suggestion that despite being beginningless, Samsara has an end. The end of Samsara is attainment of Nirvana.
The usual superficial understanding of these is to assume that one can escape Samsara, stop the round of deaths-and-rebirth, and effectively spend the rest of eternity in a state of perpetual lack of suffering.
Such answer though would omit a very important construct of Buddhism, one of "Three Marks of Existence"
According to Buddha, existence inevitably has the characteristics of

Impermanence
Suffering
Selflessness (nonsubstantiality)

Which means, a state of perpetual lack of suffering would contradict the fundamental law of the universe (as presented in the Three Marks). How could it be perpetual given the impermanence? How can suffering cease, given that suffering is an intrinsic characteristic of existence? How can I spend the rest of eternity in this state if "I" (self) does not exist?
This seems like a serious contradiction. And yet Buddha insists, there is a way to solve this conundrum, there is a way to attain Nirvana.
Without giving too much away, I would like to hint at the direction the answer lies in:
Samsara begins when subject and object separate from each other. Samsara ends when subject and object are no longer separated. The answer lies in the realm of phenomenological experience, including experience of suffering, life, and death. Good luck with your quest!

Could you elaborate on this? The exact meaning of your answer is probably obvious to experienced Buddhist practitioners, but it is unclear to me what "subject" and "object" are in this context.

It would at least be good if you could provide a source to back up your answer, though it does sound intriguing :)

this is an important methodological question @Yuttadhammo -- are we saying it is a requirement to back all our answers with sources, or is it enough to go by experience and "general understanding"

Not necessarily, but one sentence answers provide very little in the way of benefit to the person asking the question; opinions and personal experience based answers are similarly unlikely to help much. Definitely this answer is too brief to be of much use, and so it was flagged as "low-quality".

Please see meta discussion here: http://meta.buddhism.stackexchange.com/questions/26/should-we-allow-encourage-short-enigmatic-answers/

Buddhism basically deals with the present. Dwelling the mind on past or future unnecessarily creates mental vexation. Hence, concepts like God, origin, etc. are not dealt in Buddhism. It doesn't matter why or how the samsara came into existence, what matters is that samsara does exist. Now when samsara exists and we exist, our effort should be eradicating problems that give rise to suffering. For example, because you are thinking about the origin, you are to some amount troubled by the question. So as per Buddhism you should not focus your mind on such irrelevant questions as they unnecessarily create suffering.
However, if you are really looking for answers then you should consider studying the philosophy of other religions. If you do, then you will find the answer to be God. Then the question of starting point of God will arise in your mind. If you look into science, it says Big Bang is the starting point. But in my view, Nothing is the starting point. Only that which has come to exist can have a starting point. How can that which doesn't even exist have a starting point? I know this sounds ambiguous, but it's hard to explain here in few words. You can check the following link if you like, but my findings there is based on Vedic scriptures: http://shunyavada.com/


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Learning materials for Dependent Origination (Paṭiccasamuppāda) in Theravada Buddhism
I am listening through the talks and guided meditations from the retreat at Amaravati Just One More: Dependent Origination and the Cycles of Addiction Retreat, where there are a number of references to the teachings, and using them in meditation. However, although I've found many websites referencing the Paṭiccasamuppāda, I've been unable to find study materials for learning how to practically use the teachings.
Not having any teacher nearby, I have been looking online for materials. Wikipedia mentions the Twelve Nidānas, but that resource is mostly fact oriented, which is not what I am looking for. Can anyone direct me towards any online materials (website, pdf, audio, video) that help develop techniques in this area?
EDIT for clarification. There are many writings on the subject, and many try to explain the concepts of dependent origination. However, this question is regarding finding practical instructions to applying the teachings in meditation. In other words, instead of focusing on acquiring some intellectual "understanding" of the teachings, I am following the "see for yourself" approach, by not taking anyone's word for granted. Instead, using the teachings to access the wisdom they describe.
In essence, it's like being thirsty, and finding a sign saying "water this way ->". You have the choice to walk the path leading to the water, and drink, or study the sign, which won't leave you any less thirsty.

Here's a few of resources from our tradition:
http://www.aimwell.org/dependentorigination.html - a book by the Mahasi Sayadaw, one of Burma's greatest meditation teachers
https://www.youtube.com/watch?v=n_llBSCXt6c - a video by me, some monk from the Internet
http://www.sirimangalo.org/teachings/lessons-in-practical-buddhism/practical-dependent-origination/ - a written piece based on the above video.
You'll find a lot of stuff centring on the debate over three-life/one-life, which is terribly unhelpful, IMO. Here's a piece I appreciated from one of Thailand's top scholar monks:
http://www.dhammatalks.net/Books3/Payutto_Bhikkhu_Dependent_Origination.htm
Edit: here's something I wrote about practical application of PS:
http://yuttadhammo.sirimangalo.org/2009/07/three-teachers-or-buddhist-addiction.html

a few reflections on your answer. Most of the resources respond to "what is it?", whereas I am looking for "how to practically use it?". Real life practice in techniques and guided meditations, for example. Also, links from that YouTube video are broken, just FYI.

You don't actually practice dependent origination... It's something you realize through insight practice. Here's something i wrote, though, about practice according to it: http://yuttadhammo.sirimangalo.org/2009/07/three-teachers-or-buddhist-addiction.html

In one or more of the talks / guided meditations from the retreat linked to in the question, Ajahn Amaro uses the teaching quite skillfully (in my humble opinion) with reflection on a single condition at a time. These types of methods are the background to asking the question.

If you include the title of the article in the hyperlink, and/or a direct quote from the article's content, then there's a possibility that people can find the article again even if the link becomes broken. How should we deal with broken links on posts?

Two most interesting pieces of analysis I found are

Nanavira Thera's Notes on Dhamma (http://www.nanavira.org/notes-on-dhamma/paticcasamuppada)

and

Buddhadasa's "Practical Dependent Origination" (http://buddhasociety.com/online-books/buddhadasa-bhikkhu-paticcasamuppada-21-2#TOC and http://www.dhammatalks.net/Books6/Bhikkhu_Buddhadasa_Paticcasamuppada.htm)

a decent bibliography can be found at the end of Dhivan Thomas Jones' "New Light On The Twelve Nidanas" (http://www.academia.edu/2593517/New_Light_on_the_Twelve_Nidanas)

The best and most detailed explanation of paticcasamuppada I know of is in Buddhagosa's Visuddhimagga. There is an English translation by Bh. Nanamoli in the book The Path of Purification (free pdf, look at chapter XVII: Dependent Origination).

You need to be very careful when you find teaching materials on the internet specially for Paṭiccasamuppāda. It is core of Buddhism (someone had name it The Theory of Everything). The problem is lot of authors had been expressed their personal perspectives than to root of Lord Buddha's teaching so you may get confused when you compare each of them, Good luck!!

http://www.academia.edu/4990731/Two_Doctrines_of_Conditionality_in_Theravada_Tradition_Paticcasamuppada_and_Pathana-Naya
http://en.dhammadana.org/dhamma/paticca_samuppada.htm

Thank you for your answer. Yes, I am very selective in which teachings to consume. I am not interested in the theory as a doctrine, but in practical teachings with instructions that can be put to use. Perhaps this was unclear in the question?

Good question. I still have the book to this very day, but I still haven't finished reading it.
Why, because I have been taking my time on it. And it has been years since I first acquired it.
I would like to share what I experience by reading the book and so hopefully you could take pieces from here and there and piece them towards your solution.
Again, I have not finished reading it, but one thing I do know:
Don't follow affixed on the words, the physical practices or forms it may mention.
The whole practice is supposed to be a guide, words are guides as well as forms may it be bodily, mindfully or expressively, for every of these should be abandoned at the end (beginning) when one is "awoken".
Hence, may I suggest, if it teaches us this way as mentioned, we shall convey it to others likewise. It is not about the type of incense we burn, the body must not have to be perfectly sat down with legs equally crossed, music needn't be of certain type and the most important of all - words and meanings (doctrine) needn't be studied word for word when one is stuck at certain chapter / point. Let it rest, come back to it later.
Again, all words and wordings are guides and should be abandoned eventually.
For Buddhism, I often find that the best teaching and learning experience is when one doesn't feel or make others feel "special" or "different" than others during the journey of teaching / learning. If not, ego is therefore proven to still exist and with this as attachment, understanding is still not acquired.
Thanks for the question.

Thanks for the answer, quite in line with my perspective. Could you please specify the book you are referring to?

Hey, this is the same Buddhadasa guy that I referenced in my answer. I kinda like his perspective.

Following might be of some help as references:

Dependent Arising by Piya Tan essay
Dependent Arising by Piya Tan talk on YouTube
Vibhanga Sutta
Maha Nidana Sutta
Na Tumha Sutta

From the Theravada tradition:
There is a audio dhamma talk by Ven. Bhikkhu Bodhi called "Dependent Origination" which can be found here.
Here is also some text material about Dependent Origination, also from Ven. Bhikkhu Bodi:

Dependent Arising
Dependent Arising : Patticca Samuppada

Lastly there is an audio dhamma talk called "Dependent Origination" by Ajahn Punnadhammo which can be found here.
Lanka

Thanisarro's internet PDF called: 'Shape of Suffering' is the only publication I know of that provides a practical guided meditation through each of the conditions. Buddhadasa's work is good but 'Shape of Suffering' is the most practical. If you follow the meditation guidance in 'Shape of Suffering', you can decide for yourself whether the explanation is true or not.  Most of the other interpretations are mere unverifiable meta-physical theories. Regards


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What's the value or harm of a literal belief in rebirth?
Whenever I examine the concept of rebirth in Buddhism, I cannot help it but feel great skepticism.
To put it in my own clumsy words, we have many fears and one of the greatest is to cease to exist. The solution that I have found in Buddhist teachings is to outgrow that fear in particular and fear as whole, while you're at it.
In contrast to that, religions commonly introduce some concept of life after death. Which I think is a just a very comfortable delusion, self-induced to cope with this primordial fear and with the loss of loved ones.
What strikes me is that "Buddhists" talk quite a lot about rebirth and will actually give extremely precise and concrete responses to questions on rebirth, that can quite obviously not be challenged by the examining mind. It is my (limited) understanding though at its very core (if such a thing exists) Buddhism generally denies to answer any questions that cannot actually be challenged and particularly denies to answer this question.
I feel that much is to be gained from the concept of rebirth if explored as a metaphor, but it is my impression that believing it literally is diverting attention from the here and now and more practical aspects of Buddhist practice, thus ultimately being harmful. It seems to me like failure to remove the poisoned arrow.
At the same time it makes me nervous that I cannot see any truth in more physical and concrete notions of rebirth, because it's far more likely that I am just blind, rather than everybody else being deluded. So: what is it that I am missing? What do I gain if I embrace the belief that "I" will roam this world in a new body once this one dies?

Your question sort of implies that you're considering the persistence of consciousness in rebirth, but I'm not entirely certain that's what you intended, or am I off a bit in reading it?

@TimPost: I'm not that certain either. But I am less concerned with the "how" of rebirth as to "why" I would actually explore any such notion. To me it seems to divert attention from the here and now and to give an excuse for postponing living. But quite possibly it adds another quality and that's what I am seeking to find out about.

Is this a question or an answer disguised as question? ;)

@zvolkov: No, it is a question. I see that I probably spent too much time describing my view on things, but I wanted to draw the line between what I do gain from the concept of rebirth as opposed to the things that elude me (which is what I want to learn about). Also it was an invitation to criticism of what I believe to "understand" thus far, which Sankha Kulathantille accepted.

This would be a good starting thread on a forum, but it is a bad Question for a Q&A site (i.e. I can't quickly pin down what you are asking, I'm not sure what would result in an answer you could accept)

While I should probably get rid of some of the noise, I did end on a relatively clear question. Please feel free to suggest an edit that gets rid of non-essential/unclear/distracting parts. As explained in a prior comment, I was hoping that my ramblings could explain that I am not questioning that rebirth as a concept has no value, just that I would like to learn more about the value of the quite literal interpretation that many Buddhists adhere to.

Maybe changing the title to "What's the value of belief in rebirth?" or some such thing. Good if you can clean up the question a bit... do you really need so much background just to ask the question?

"I" is an illusion according to Buddhism. So your "I" isn't the roamer.

I think you're right to question the importance of rebirth; the Buddha himself didn't seem to dwell on the concept, though remembering one's past lives does have obvious practical benefits - lots more experience to draw upon :)
Bhikkhu Bodhi wrote a couple of things about the subject you might find interesting:

Dhamma Without Rebirth?
Does Rebirth Make Sense?

As he says in the first link,

If we suspend our own predilections for the moment and instead go directly to our sources, we come upon the indisputable fact that the Buddha himself taught rebirth and taught it as a basic tenet of his teaching. Viewed in their totality, the Buddha's discourses show us that far from being a mere concession to the outlook prevalent in his time or an Asiatic cultural contrivance, the doctrine of rebirth has tremendous implications for the entire course of Dhamma practice, affecting both the aim with which the practice is taken up and the motivation with which it is followed through to completion.

I've talked about the subject before myself, and the conclusion I make is that it's not that Buddhists believe in rebirth, it's that we don't believe in death - the latter being merely a concept referring to the change from one set of experiences to another. True death only occurs either at every moment or at the experience of nibbana.
In any case, as useful as rebirth may be in reminding us of what's really at stake in our dhamma practice, far more useful is an understanding of the present moment, something that really has little to do with past or future lives.

amazing question and answer:). This is what we expect from this forum.

I guess my question is just poor to get the answer I seek. But this one is great none the less. Particularly "True death only occurs either at every moment or at the experience of nibbana." nails it for me ;)

If you are into Vipassana meditation, you must have noticed that experiences rise and cease one after the other. When one experience ceases, another will arise. It doesn't stop! Likewise, death is also another experience in reality. It doesn't prevent the next experience from arising as long as the causes for arising haven't been eliminated.
I recommend you to go through the "rebirth/reincarnation" Q&A section at http://video.sirimangalo.org.
Some questions are unanswered in Buddhism for several reasons:

It doesn't lead to end of suffering.
The question is based on a false hypothesis. So the question itself becomes meaningless or false.
Only a fully enlightened Buddha can realize the truth of it.

"Becoming one with the world" can be misleading as it can imply the Hindu concept of the universal soul. The Buddhist teaching is that you are just another process of causes and effects which are impermanent, subjected to suffering and devoid of any self or inherent value. Just like everything else in the universe.

Thank you @Sankha Kulathantille, I will pay attention to your answers from now on :)

The Buddha said never to accept something just because it was said, but to seek an answer to these questions yourself.
If you don't know for sure either way. There is no need to believe anything either way.

I understand that there is no need. Still I am interested in what I could gain from embracing such a belief.

Belief is attachment. Questions like whether rebirth is true or not are red herrings on the path to truth. What primarily matters is not the truth of such a question, but your relationship to the question, and whether that relationship is based in REALITY in you.

If I understand your question correctly, maybe the following notes may be of concern:
Buddhism as a philosophical current or religion evolved out of an ascetic movement that was very much concerned with personal salvation, the so-called śramaṇa-movement. Apart from buddhism, the relics of this movement is the Jaina religion and historically a religion/philosophy called Ājīvika, which died out only about a thousand years ago. But also the mainstream orthodox Hindu schools of philosophy owe very much to this movement. Stories of wandering ascetics questioning the Buddha about his doctrine, arguing with him or stories of the Buddha, who at the sight of ascetics warns or teaches to his followers abound.
In this movement, rebirth was more or less totally taken for granted (some exceptions, the materialists for example, exist), it was common sense. That is why in Buddhism you can find the same attitude. People critized and attacked the Buddha on grounds of his specific doctrines (most notably rebirth without soul - anattā/anātman) but they hardly ever or never doubt rebirth as a concept. Since the Buddhist scriptures very much reflect the philosophical discussions of the time of the Buddha (and after), there was just no need, to give reasons, explanations, proof for rebirth.
In the Samaññaphalasutta a lot of rival views are examined by the Buddha, you might check there, if the materialists are quoted denying rebirth and what the answer of the Buddha was and whether he actually defended the concept of rebirth in any way.
This can be summed up by quoting from Yuttadhammo's answer:

it's not that Buddhists believe in rebirth, it's that we don't believe in death

Concerning the unanswered questions, I guess the one in concern would be, whether the tathāgata lives on after death. This, though refers to an enlightened being, someone who has attained nirvāṇa and so has left the cycle of rebirth. So, strictly speaking, it is not a question about rebirth. And by the way, as far as I understand the scriptures, the Buddha denied to answer these questions or simply remained silent, when asked, because the question cannot be answered correctly in words. Other questions were refused to answer, because the Buddha did not intend metaphysics or anything that was not considered conducive to salvation, liberation.
Now, to conclude, the notion of rebirth is totally central to Buddhism, since Buddhism essentially is a response to the perceived fact of rebirth, that has, as has all life, the characteristic of being laden with (within the bounds of the samsaric cycle) unescapable sorrow. Essentially, the Buddha didn't teach a happier mode of life, but that all life is bound to be miserable and the way out is the way out of life (which in this case does not mean death, but nirvāṇa).

Thanks. Yes, I think Buddhism considers rebirth a problem/the problem of human condition, which is 'solved' by Buddhist practice.


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What is required to achieve Nirvana in Buddhism?
Nirvana is considered by many religions the pinnacle to strive for.  What do I need to do to achieve Nirvana?  Are there different perceptions of the requirements held by different sects?

sorry if i sound trite, but just practice

To answer your question let me draw an analogy. What is required to become a professor?
According to Wikipedia, "A professor is a highly accomplished and recognized academic, and the title is in most cases awarded only after decades of scholarly work to senior academics". Being a professor is not a concrete state, it is a label they put on years of hard work, culminating in professional realization.
Similarly, Nirvana is not a concrete state, it is a common name for the condition of a highly accomplished spiritual practitioner. This condition is not something you can contrive knowing the requirements, it is a result of years of personal transformation.
Nirvana can be characterized as condition of having transcended suffering & death. The requirement for this is said to be a complete cessation of Attraction (obsessing over something as desirable), Rejection (obsessing over something as undesirable), and Ignorance (mistaken understanding of how everything works). One of the key components of Ignorance is a deeply lying conviction in existence of substantial self and a tangle of reflexes that grow around that. Much of Mahayana practice is targeted at destroying this belief, not just at conceptual level, but at the level of basic day-to-day instincts.
If we could simplify the requirement for becoming a professor to "complete cessation of ignorance in the field of study one specializes in", we could perhaps make a stretch and define Nirvana as "complete cessation of ego complex, along with negative experiences and behavioral tendencies it generates". As any simplification, this is not entirely accurate: just as becoming a professor requires tons of practical skill and experience outside of the primary field of study, attaining Nirvana requires cessation of all mental and emotional obscurations, a tendency to get stuck on anything, not just on self.
Now, for the purposes of this discussion I'm equating Nirvana with Enlightenment, which depending on a school may or may not be the right thing to do. Specifically in Mahayana, Nirvana is considered a conceptual projection (a shadow of ego so to speak) that has to be transcended as part of awakening to Self-Existing Buddha Nature (=Enlightenment).

In Buddhism you need to follow the Noble Eight Fold path to attain nirvana. It is further divided into three parts for simplicity - Sila (morality), Samadhi (mental culture) and Panna ( wisdom).
The noble eight fold path is as below :
Sila (Morality): 1) right speech 2) right action 3) right livelihood
Samadhi (mental culture): 4) right awareness 5) right concentration 6) right efforts
Panna (wisdom) : 7) right resolve 8) right view
In whichever teaching the components of Noble Eight Fold path is found there you will find source of Nirvana. So you can follow any sect you prefer. But right view is what differs in Buddhism which takes you in right direction. Understanding Buddhism's (right) view of rebirth, karma and three realities of life (impermanence, no soul and suffering) and dependent origination can help understand Nirvana better.

Good and precise answer.

I am reading a book called What the Buddha Taught by Dr. Walpola Sri  Rahula.
Noble Eightfold Path
The Fourth Noble Truth is 'The Path' (Magga) leading to the cessation of Dukkha (defined in the First Noble Truth as basically anything conditioned or in other words part of dualism; things that are not everlasting)
See other answers that already list the eight divisions/categories.
Five Hinderances
Ponder these.

lustful desires (kāmacchanda)
ill-will, hatred, or anger (vyāpāda)
torpor and languor (thīna-middha)
restlessness and worry (uddhacca-kukkucca)
sceptical doubts (vicikicchā)

Seven Factors of Enlightenment
Meditate on these.

Mindfulness (sati) i.e. to be aware and mindful in all activities and movements both physical and mental.
Investigation and research into the various problems of doctrine (dhamma-vicaya). Included here are all our religious, ethical, and
  philosophical studies, reading, researches, discussions,
  conversations, even attending lectures relating to such doctrinal
  subjects.
Energy (viriya), to work with determination till the end.
Joy (pīti), the quality quite contrary to the pessimistic, gloomy, or melancholic attitude of mind.
Relaxation (passaddhi) of both body and mind. One should not be stiff physically or mentally.
Concentration (samādhi).
Equanimity (upekkhā) i.e. to be able to face life in all its vicissitudes with calm of mind, tranquillity, without disturbance.

To cultivate these qualities the most essential thing is a genuine
  wish, will, or inclination. [...] One may also meditate on such
  subjects as the Five Aggregates investigating the question "What is
  being?" or "What is it that is called I?", or on the Four Noble
  Truths. Study and investigation of those subjects constitute this
  fourth form of meditation, which leads to the realization of Ultimate
  Truth.

Excerpt about the feeling 'I AM'

It is the vague feeling 'I AM' that creates the idea of self which has
  no corresponding reality, and to see this truth is to realize Nirvāna,
  which is not very easy. In the Samyutta-nikāya there is an
  enlightening conversation on this point between a bhikkhu named
  Khemaka and a group of bhikkhus.
These bhikkhus ask Khemaka whether he sees in the Five Aggregates any
  self or anything pertaining to a self. Khemaka relies 'No'. Then the
  bhikkhus say that, if so, he should be an Arahant free from all
  impurities. But Khemaka confesses that though he does not find in the
  Five Aggregates a self, or anything pertaining to self, 'I am not an
  Arahant free from all impurities.' O friends, with regard to the Five
  Aggregates of Attachment, I have a feeling "I AM", but I do not
  clearly see "This is I AM".' Then Khemaka explains that what he calls
  'I AM' is neither matter, sensation, perception, mental formations,
  nor consciousness, nor anything without them. But he has the feeling
  'I AM' with regard to the Five Aggregates, though he could not see
  clearly 'This is I AM'.
He says it is like the smell of a flower: it is neither the smell of
  the petals, nor the color, not of the pollen, but the smell of the
  flower. Khemata further explains that even a person who has attained
  the early stages of realization still retains this feeling 'I AM'. But
  later on, when he progresses further, this feeling of 'I AM'
  altogether disappears, just as the chemical smell of a freshly washed
  cloth disappears after a time when it is kept in a box.
This discussion was so useful and enlightening to them that at the end
  of it, the text says, all of them, including Khemata himself, became
  Arahants free from all impurities, thus finally getting rid of 'I AM'.

In Theravadan tradition you need to gain Insight through Vipassana meditation in order to attain Nirvana. That's all! Everytthing else just makes the path to Enlightenment easier or has other benefits like Samatha meditation.

Nirvana is not an achievement! According to the Buddha there is no path to it because then nirvana becomes an effect of taking that particular path. Also, no practice will lead you to nirvana. Because again, nirvana becomes the effect of the practice. If nirvana is an effect it's not the end of suffering is it? Buddha's only advice was to fully investigate, understand the cause of suffering. According to him understanding of the cause is the ending of suffering. Paths and practices were introduced by monks(not the Buddha) for their survival, existence!

Not sure about many religions. I think Hinduism and Jainism have concepts of Nirvana. But they are different from the Buddhist teaching of Nibbana. Anyways, it's so simple in Buddhism. You only need to eliminate craving to attain what Buddhists mean by 'Nibbana'. Read about the "Four Noble Truths".

what is craving?

desiring/liking/wanting

Nirvana can defined as a peaceful state of mind that is free from craving, anger and mental suffering.
So answer for, What is required to achieve Nirvana is eliminate all the above things.

Nirvana is not a one-time switch... You're in Samsara - BOOM! - you're in Nirvana and for good! It's not like that.
Nirvana is a momentary experience of freedom and peace. It can ONLY be such as there is nothing else existent but this moment. To realize such peace and freedom, it's helpful to loosen up one's attachment to desirable conditions and rejection of undesirable conditions. In other words, to loosen up your dependence on conditions overall when it comes to happiness and peace.
Through meditation practice and discipline in everyday life, it will become easier and easier to let go of our expectations, assumptions and demands that life go our way. That's not to say we don't make an effort to have favorable conditions in our lives... Not at all. That would be very anti-life and against our basic nature. We all enjoy good things and rightfully so.
But when our desire for good things becomes constant craving and strong attachment to those things, we're screwed because all good things come to an end (and are replaced by "bad things" like loss, old age, sickness and - gulp! - death). There is no peace or happiness in such craving and attachment. And there's no lack of peace or unhappiness in "bad" conditions either. But our normal approach is to loop endlessly through these cycles of craving, clinging and disappointment. It's very tiring and painful.
"Nirvana" is the momentary experience of being free of this endless cycle. It's that simple. And the more you experience this freedom, the less you will care about the changing conditions of your life and be able to flow with all of it. Yet, you are never finished with developing this capacity as it goes very deep.

I believe that all Buddhist "sects" would say that there is a path to nirvana. In deed this is the "fourth noble truth", though different "sects" interpret it differently, or at least claim that other "sects" have a different understanding of it. For your purposes, maybe that's what the long history of doctrinal debate is actually about.
I believe that all Buddhists claim that meditation is a prerequisite to nirvana, though that seems to take different forms, with different "sects" vying over e.g. the terms "sudden" and "gradual", and with different instructions and communities.
I've put 'sect' in quotes because I'm going to side with what I understand from soto zen, which I think stresses that we "don’t practice zazen in order to get enlightened, we practice being enlightened as we practice zazen". So the fukanzazengi by Dogen says:

The zazen I speak of is not learning meditation. It is simply the Dharma gate of repose and bliss, the practice-realization of totally culminated enlightenment. It is the manifestation of ultimate reality... If you concentrate your effort single-mindedly, that in itself is
  negotiating the Way

sorry if i'm completely off, just makes sense to me

This may seem lengthy to some, but it simply is. The comment above this one is correct. There are many approaches, this is the personal approach my mind went through to be able to achieve it. My body and mind achieved nirvana completely by accident when experimenting with meditation at age 17. This was brief, lasting somewhere between a half an hour and a few hours.  It sought it again and failed and wrote it off as a delusion until later. See, the approach was wrong, the WANT of nirvana itself distracted my body and mind from achieving it. The Buddhist obviously have temples where monks go to achieve it, but it seems to take years for them. So how did this body achieve it by accident on it's first occasion meditating? Well, under had a very good teacher for one. My mind was also under the influence of an African tree ash that aids in meditation. The concept of achieving nirvana without seeking it seems terribly difficult/backwards, but really that in itself is the lesson. I really wanted to stress that point.
But overall, you must devoid your mind of "right" and "wrong". You must take and see things as they are, without an opinion of it. You must learn to let go of all desire. To transcend your own ego. There are many ways to coin it, but it is in fact a personal journey that must be achieved personally. For some people, this takes many many years. If you have trouble, that just means to need more practice, and you may need to apply the practice into your outside life. A teacher helps with all this. For meditation in general you will receive benefits without achieving nirvana. To properly meditate is the beginning. This body has found that having a focus/focal point for concentration helps. My mind uses breathing. In through nose, deep into the abdomen, out through the mouth, again, as deeply as possible. My mind focuses on this. Relaxing as much as possible. Then a thought crosses my mind. I take that thought, acknowledge it, and complete it. That's the process. The key for me is to not judge, to not even have an opinion on it, to simply see it for what it is. This seems to work for others as well, but I don't claim to be a mind reader in the sense that I know every step they took to achieve this state. There are many religions, nay schools of thought, that can give you more details, but truly if you understand one grain of salt, you understand all of them. One can go and study these things, the internet is a wonderful tool. There is no right and wrong. There simply is. Accept this, work at it, and the road never ends, achieving nirvana isn't a stopping point. Do it all for self-improvement. Do not confuse stubbornness for patience.
Also, I remember the exact thought that was the focal point for turning my mind into proper thought. An old saying of proper thought, that I came across whilst reading the Tao of Jeet Kun Do by Bruce Lee. I don't know if it'll help you, I don't offer a cure all. But again, this is my personal journey.
"Empty your cup, so it may be filled."

In order to achieve Nirvana (the Theravadin version of Enlightenment) you need to do a lot of mindfulness meditation and have a lot of good karma. It is not possible to understand Nirvana in terms of modern psychology and philosophy, because Buddhist psychology is very very difficult to understand. Fortunately, you do not need to understand Buddhist psychology to achieve Enlightenment. These days, suffering is mostly caused by tragic adaptations to an abusive or dysfunctional family background, causing problems in self-love and finding love. I have written a book on mindfulness meditation, if you want to read about my 50 years of experience with traditional mindfulness meditation.

Recite & memorize kītāgirisutta:

"Monks, I do not say that the attainment of gnosis is all at once.
  Rather, the attainment of gnosis is after  respectively training,
  respectively action, respectively practice. And how is there the
  attainment of gnosis after respectively training, respectively action,
  respectively practice?

There is the case where, when conviction has arisen, one visits [a
  teacher].
Having visited, one request to be his attendant (see vinaya mahāvagga mahākhandhaka, and CH. III TAKING A MEDITATION SUBJECT of Visuddhimagga)
Having been attendant, one listen carefully.
Having listened carefully, one hears the Dhamma.
Having heard the Dhamma, one memorizes it (dhatā=sutadharo).
Having remembered by memorizing, one ponders the meaning of the teachings.
Having pondered the meaning, one comes to an agreement through
  pondering the teachings.
There being an agreement through pondering the teachings, wish-to-do
  arises.
When wishing-to-do has arisen, one exerts.
When one exerted (an effort), one meditates insight.
Having meditated insight, one dedicates his life.
Having dedicated his life, one realizes with the mind (discernment's body) the ultimate truth and, having penetrated,
  enlightened, it with discernment, sees it.

"Now, monks, there hasn't been that conviction, there hasn't been that
  visiting, there hasn't been that attending ... that listening
  carefully ... that hearing of the Dhamma ... that memorizing ... that
  penetration of the meaning of the teachings ... that agreement through
  pondering the teachings ... that wishing-to-do ... that effort ...
  that meditating insight ... that dedicating his life. You have lost
  the way, monks. You have gone the wrong way, monks. How far have you
  strayed, foolish men (moghapurisa), from this Dhamma & Discipline!

I have edited many part of the translated sutta follow to many pali of many sutta and commentaries. I wish the editing makes easier for the reader to connect the sequence of steps.

You should include the original author and translator's names with your quote.

@JamesJenkins I'm sorry. my English is terrible, so I don't understand what do you mean. I already included translation link above. However I'm not recommend because the tanslation have not connect the words each other inside the same Sutta enough.  Also, the original version not compatibility with other sutta and commentary. I have not a good English skill, but I can read pali and commentary. I can connect them together without cutting off.

"The Buddha once said, let an observant person come who is honest and no deceiver, and he would teach that person the Dhamma. Those are his prerequisites for anyone who was going to practice and get results. If you’re not honest with yourself, you’ll start to deny things that are arising and passing away in the mind. And if you’re not observant, it all goes right past you.

This means that the Dhamma is something special. The discernment of the Dhamma is something special. It’s not something you can figure out by reading books and being clever. It requires good qualities of the heart, and in particular this quality of honesty, which is basic to all the other good qualities you need. So make sure that honesty enters into the mix as well. That’s how the discernment becomes penetrating, as the Buddha says, leading to the right ending of suffering and stress."

~ Thanissaro Bhikkhu "Developing Discernment" https://www.dhammatalks.org/Archive/Writings/CrossIndexed/Published/Meditations9/090804_Developing_Discernment.pdf

I would believe not even one answer unless one makes the experience for oneself. Be even skeptical that Nirvana exists, for there is no real evidence unless one is experiencing it. Just because the Buddha said it "exists" doesn't make it so. All people answer as if they are enlightened or made the experience .. hell as if they are expert on this field but they are not. If nirvana really exists it must be possible to see it under a fmri. Why? If one really abandoned greed, hatred and delusion one can expose the "enlightened" person with evocative material to see whether any greed, hatred or delusion appears in the brain. I'm positive that there will.

People tested some monks with FMRIs, years ago: http://www.cbc.ca/news2/background/meditation/

So what? They still need to get exposed with vivid evocative stimuli to see whether their brains are responding to let's say sensual material. I'm aware that scientist tested monks but it wasn't about being enlightened.

Thanks for clarifying -- I didn't even notice that wasn't in that CBC report of an MRI test. The kind of testing which was reported seems to me more impressive (more difficult and more useful), i.e. to remain "happy" when exposed to "unpleasant sounds and images", than dispassionate towards sensual material -- an unconditioned absence of dukkha.


text:
What are the main differences between the Theravada, Mahayana and Vajrayana branches of Buddhism?
The question basically says it all, but I'll try to elaborate a bit:
Are there differences in terms of the concepts used in each of these branches?
Are there differences in the practices of each of the branches?
Or are the differences between each of the branches simply explained in terms of historical or geographical factors?

Unfortunately there are various and contrary views about that differences around. Have you ever tried to discern the mentioned differences from the wikipedia-article? And from its history-records? And there's a lot of buddhistic and non-buddhistic material online which deal with that question in this or that way - and even I myself feel tempted to give a viewpoint, just now... I'd say that question is much too broad for the Stackexchange-platform.

It's time to test the waters anyway, so I thought it'd be the right time to ask this. If it is deemed too broad by the community, so be it :)

It's a big question to answer however I think it has be done.

Yes, I think it is too broad; maybe it would make a good wiki post? Anyway, given its the sort of thing you'd find on Wikipedia, I'm guessing it's not proper for an expert exchange site like this.

This question, indeed, requires a whole book in order to be answered completely. Let me address only Theravada and Mahayana here.
In two words:

The most important aspect is that Theravada is focused on your own liberation from suffering, while Mahayana is targeted to all sentient creatures;
There are many consequences here:

Theravada assumes that you have to practice for yourself, while others can only suggest you. Mahayana says that you can (and have to) share your experience and accomplishments with others, thus making followers for yourself;
Theravada suggests to seek enlightenment for yourself first; Mahayana is up to delaying breaking off Samsara in order to help others;
Theravada practices are mostly silent and very personal while in Mahayana it is more often "wrapped" in some collective rituals like chanting;

In Theravada, the final goal for a Bodhisattva is nirvana. In Mahayana, prominence is important by itself;
Each teaching is more or less localized, e.g. at a certain country/territory there's usually only one;
If you'd like to read scriptures in original language, you should be aware that Theravada is written in Pali (Pali Cannon) while Mahayana is written in Sanskrit (Sutras);

Of course, there are also big differences in texts, ritual, etiquette, and so on.
This Comparative Study between two traditions provide with greater details.

As @bytebuster said, this could take an expert a book to answer. But in the spirit of constructive collaboration, let me throw in my two cents:
In Theravada, the focus is on escaping from Samsara to Nirvana, mainly through attaining perfect control of your mind, which in day-to-day life manifests as practice of minimalism.
In Mahayana, the focus is on transcending the dichotomy of Nirvana/Samsara, and realizing the Buddha Nature, mainly through deconstructing the ego; in day-to-day life this manifests as practice of altruism and non-attachment.
In Vajrayana, the focus is on liberating the mind from mental and emotional obscurations so that it can fully enjoy the Natural Perfection that does not need to be attained.

Old answer, not precise.


text:
Does rebirth or reincarnation occur in Buddhism?
How is the concept of rebirth or reincarnation handled in Buddhism? Does it occur? Will everyone be reborn? Are people always reborn as people?

That's actually four questions... see http://meta.stackexchange.com/a/98802/161650

Nearly five questions, since the assumption that rebirth is the same as reincarnation - separate concepts as I've seen them explained. Rebirth occurs, reincarnation not, say some (Theravada at least) teachers. Depends on your definition of the terms as well, of course. :-)

You might want to check this (earlier) thread also: http://buddhism.stackexchange.com/questions/1/is-there-an-equivalent-of-heaven-and-hell-in-buddhism

Disclaimer: My answer to this will be non-exhaustive. My answer will be scoped as close to that of the question as possible. (General). I will also answer your question (which is actually 4) piece by piece.

You asked:

Does reincarnation/rebirth occur in Buddhism?

Yes it does. The concept of rebirth and reincarnation in Buddhism is complex and can differ slightly or largely from tradition to tradition however.
You asked:

Will everyone be reborn?

Every sentient being (people, animals, etc) is in a cycle of rebirth. They will all be reborn after death. The only exclusion to this will depend on the tradition. Most traditions, in a general sense, state that one may leave the cycle of rebirth if they attain enlightenment or nirvana. This is only possible when you are a human, though.
You asked:

Are people always reborn as people?

The answer is no. Please see next section of this answer for elaboration.
You asked:

How is rebirth/reincarnation handled in Buddhism?

In Buddhism, there exists the concept of Samsara. This is the continuous cycle of rebirth throughout six different realms. These realms include the realm of Gods, Titans, Hungry Ghosts, Hell, Animals, and Humans. One may be considered more preferable to another, for example Gods to Hell, yet all are imperfect and involve some level of suffering. Depending on past lives and karma, one will move from realm to realm during each rebirth. The Human realm is generally considered to be the best because it is the only one in which one may obtain enlightenment and exit from this wheel of Samsara and therefore end the cycle of rebirth and suffering.
For more information, you may find this article to be useful.

Side Note: My professor of Eastern Religions once told me that being in this cycle of rebirth can be a great source of anxiety, hence one source of motivation to exit from it.

Simple answers for last three questions as far as I know,
Does it occur ? Yes it is
Will everyone ? Yes until someone attain Nibbana
always as people ? No, it can be any(animals/human etc)
But the first question is too broad to answer.
You can find more details in this article about recantation.
Simple explanation for recantation as according to that article,

Reincarnation is not a simple physical birth of a person; for
  instance, John being reborn as a cat in the next life. In this case
  John possesses an immortal soul which transforms to the form of a cat
  after his death. This cycle is repeated over and over again. Or if he
  is lucky, he will be reborn as a human being.

How is the concept of rebirth or reincarnation handled in Buddhism?
  Does it occur? Will everyone be reborn? Are people always reborn as
  people?

Strictly speaking there is no reincarnation in Buddhism, but rebirth is. 'Reincarnation' imply idea that some constant Soul incarnates into being, which 'rebirth' does not imply. Moreover, Buddhist teaching deny existence of such constant Soul. After death, new being is born, who causally related to past being and carry on actions of past births. Everyone, except who attained final Nirvana, rebirths in almost any place in the Cosmos depending on his/her past actions (karma).