Are Matthew, Mark and Luke the same book in different version? I always thought Matthew, Mark and Luke are different books originally were written by different people. But recently I was told that Matthew, Mark and Luke are originally the same book but in different versions. At the beginning there was one book only and then it was edited or adjusted by different people so at the end we left with three versions of the same book. Is it true?
Matthew, Mark, and Luke, aka the Synoptic Gospels, share common elements and parallels and were written by different people for different audiences. Your question has been (and still is) debated among Biblical scholars. My answer is, at best, a brief summary with some pointers to references that may be helpful and some encouragement for you. 

Mark is believed by most scholars to be the earliest written account. There is evidence to suggest that Matthew and Luke borrowed from Mark. There is also evidence for a lost book of Jesus' sayings, known as Q, that influenced Matthew and Luke. 

To say that they are different versions of the same original book does not address the historical origins of ancient manuscripts, oral traditions, the historical contexts for which they were written, and the editorial practices that created the manuscripts from which our modern translations were (and are) derived. 

What you were told--that there was one original book--may be an attempt to support Biblical literalism and inerrancy and to say that there once was one original and perfect manuscript. This view is more commonly held within American evangelicalism. 

Each Gospel stands on its own and has profound lessons for Christians. The study of scripture can be a rich and fulfilling activity. 

A useful reference in studying the Synoptic Gospels, specifically the parallels among them, is "Gospel Parallels: a Comparison of the Synoptic Gospels" by Burton H. Throckmorton. 
https://www.amazon.com/dp/0840774842/

Another book that covers the doctrines of Christian scripture is "Inspiration and Authority: Nature and Function of Christian Scripture" by Paul Achtemeier. 
https://www.amazon.com/dp/0801045428/

For deeper study, the "New Interpreter's Bible Commentary" in 10 volumes is an excellent resource. 
https://www.amazon.com//dp/1426739125/