In the holy Quran, Quran is mentioned numerous time as the book
It is He who has sent down to you, [O Muhammad], the Book; (3:7)
In the last sermon of the prophet, the prophet said
I leave behind me two things, the QUR'AN and my example, the SUNNAH and if you follow these you will never go astray.
But Quran was never compiled as book in the life of Muhammad (PBUH). Why was it left out of the book form when the Quran itself refer to it as a book?
The revelation of Quran took 23 years and it had continued to the last year of the Prophet Muhammad's(PBUH) life. So nobody was able to compile it as a book during the Phrophet's life, since it was not complete.
But after the Prophet's demise everyone knew that the revelation had finished and Quran was not going to change anymore(no ayah would be added).
So at that time they collected all those scripts written by sahaba and compiled it.
The written compilation process did not take place during the prophet's time as revelations were an ongoing process. Manuscripts were not generated clearly earlier in his time. However, it was still recorded in bits and pieces.
From a historian point of view, citing islamic written material as reliable is difficult based on the theory that the complete compilation of the Quran was only seen in the 8th century, a century after Muhammad's death . Historical evidences (Historical Archaeology method) are evaluated based on textual sources: inscriptions, archival documents, narrative histories, law codes and guidebooks that support the main source (Quran in this example).
In the Muqaddimah, Ibn Khaldun warned of seven mistakes that he thought that historians regularly committed. In this criticism, he approached the past as strange and in need of interpretation. The originality of Ibn Khaldun was to claim that the cultural difference of another age must govern the evaluation of relevant historical material, to distinguish the principles according to which it might be possible to attempt the evaluation, and lastly, to feel the need for experience, in addition to rational principles, in order to assess a culture of the past. Ibn Khaldun often criticized "idle superstition and uncritical acceptance of historical data." As a result, he introduced a scientific method to the study of history, which was considered something "new to his age", and he often referred to it as his "new science", now associated with historiography. His historical method also laid the groundwork for the observation of the role of state, communication, propaganda and systematic bias in history, and he is thus considered to be the "father of historiography" or the "father of the philosophy of history". https://en.wikipedia.org/wiki/Historiography_of_early_Islam#7th-century_Islamic_sources
With that said, the scientific method of historical manuscripts as evidences alone are not suitable for the compilation of the complete quran as you must understand that the arabs at the time did not have any paper. Paper, originally, was brought by the Muslims from China.
"It followed the battle of Tallas (751) fought between Chinese and Muslims, when Chinese prisoners revealed the secret of papermaking to the Muslims. From an art, the Muslims developed it into a major industry." http://www.muslimheritage.com/article/beginning-paper-industry
Location of the Quranic material included parchments, scapula, leafstalks of date palms and from the memories of men. Thus most of the written items before the Quran had disintegrated with time. In addition, it was discouraged to make coins or any form of adornments related to the prophet as it may mislead people to worship him instead. The difference in culture and civilization and limited access to academic tools like paper contributed to the little amount of manuscripts available. "Before the Quran was commonly available in written form, speaking it from memory prevailed as the mode of teaching it to others. The practice of memorizing the whole Quran is still practiced among Muslims. Millions of people have memorized the entire Quran in its original Arabic. This fact, taken in the context of 7th-century Arabia, was not an extraordinary feat. People of that time had a penchant for recited poetry and had developed their skills in memorization to a remarkable degree. Events and competitions that featured the recitation of elaborate poetry were of great interest". https://en.wikipedia.org/wiki/History_of_the_Quran
What sets the quran apart from this was that, interpretation was strictly excluded to retain the purity of the material. People may then relate to the hadith for the majority agreed interpretation if they could not understand properly. In a way the Quran is unique in that it is the only source of its own with any sources before it to be of little importance as every detail were confirmed and recorded in the Quran. Further interpretation are to be based on human judgement or tradition in a separate book, thus preventing the corruption of the intended material. Interpretation is subjective depending on the person's level of experience, intellect and understanding.It is understandable if people discredit its credibility but it is important to understand the lack of writing technology that contributed to the late written entry of the Quran, hadith etc. Nevertheless, the practice of standardization had to be commended for it ensured that there is a clear distinction between what was confirmed and what was not. In addition of the oral authenticity, witness matching was to a certain extent, evidence of reliability.
http://www.quranreading.com/blog/the-history-of-revelation-and-compilation-of-quran/
There were no solid manuscripts that contributed to the production of the Quran, but as I said, the Quran is a unique form of literature with unorthodox, advanced authentication practices that were not seen in the early few centuries. Quran is unique in that it is the only source of its own and required majority voting of a group for authentication purposes justifying its written distribution unlike most religious material that were written and confirmed only by a few., thus compiling at a later time made more sense was made even more urgent when war killed most of the Quran reciters.
Quran comes from the root word "Qirat" which means recitation. So the Prophet (pbuh) gave the Quran in the form of a recitation. "Al-Quran" means "THE RECITATION".
The first word revealed of the Quran was "IQRA", which means "Recite".
Recite in the name of your Lord, Who created- Created man, out of a (mere) clot of congealed blood (Quran 96:1-2)
But the Quran (recitation) is in the form of a Book with Allah. The following verses indicate that...
Ha, Meem. By the clear Book, Indeed, We have made it an Arabic Qur'an that you might understand. And indeed it is, in the Mother of the Book with Us, exalted and full of wisdom. (Quran 43:1-4)
The Quran clearly indicates "We have made it an Arabic Quran", so it is THAT BOOK that is made into a recitation and given to us in Arabic. Allah has the "Mother of the Book".
Today the Quran exists in books but also exists in the hearts of millions of Muslims who know it by heart it. We have the "hafiz", who is a person that knows the whole Quran by heart.
The main aim of the Quran is to learn by heart, but to assist in learning it, people would write it down as it was being revealed to the Prophet (pbuh). It was written on wood, leather etc. by different people. But 19 years after the Prophet (pbuh) passed away the Khalifah Uthman(ra) realized that there were too many of these pieces that were floating around and could cause corruption or loss of text. Hence he gathered all those small pieces together and burnt them. The Muslims formed a committee and compiled a standard version. This was in presence of Uthaman(ra), Ali(ra) and many other people who were present always beside the Prophet(pbuh) when the Quran was revealed or had learnt the entire Quran by heart under the Prophet(pbuh). This was easily compiled as all of them knew the Quran entirely by heart.
This compiled version is still present in Turkey.
According to Shia Quran was compiled at life of prophet by Imam Ali as. He came to home of prophet every night and said Salam. If heard reply entered and if not backed.
At nights prophet said the Quran to Ali as and he wrote them on animal skins.
Also at time of Government of Uthman ordered to all cities that all Qur'an should be collected and burnt them all. But Ali sa did not obey and did not deliver his Quran to be burnt and kept it.
Also Quran was protected by memorizing it by hundreds of sahaba and even if no written Quran existed still it survived by high number of Quran memorizes.
This Quran also has comments of Gabriel about verses of Quran told to prophet and its volume is 3 times of Quran only. This Quran was on separated animal skins and prophet before his death said to Ali as whe I died remain at home and collect my Quran and make it compiled. When Ali as finished compile took it to mosque and said to Sahab this is Quran of prophet. They said we have our own Quran and do not need it. (In commentaries of that Quran there was some interprets about Caliphet of Ali as) then Ali as said you will never see this Quran. this Quran passed to next Imams and now it is with Imam Mahdi a.s. each Imam said parts of it to their students and thy wrote 400 books based on them and those 400 formed knowledge and Fiqh of Shia.
Lots of Sunni references can be found in this page:
The Quran was revealed during the time of the Prophet Muhammads (saws) lifetime. Many verses came down and pertained to that period in time for the Muslims.
One example is when Allah mentioned the Prophet saws and his siddiq (Abu bakr) in the cave going towards Madinah. Surat Al Tawbah 9:40
The Quran was relayed through oral tradition and was memorized by those who heard it and also written on palm leaves. There are many reasons why it wasn't compiled during the time of the Prophet saws, books can be lost like we've seen with previous books of Allah when families were stripped of their rights to carry the Torah or Bible in their homes. The Quran was memorized immediately and was undisputed. Every single Muslim could vouch for every single letter in the Quran. So much so that if one letter was omitted they would burn that whole batch of books.
The compilation was done during the time of Abu Bakr when so many companions who memorized the Quran were dying, Omar al Khattab plead the case that it needed to be written down and standardized. Abu Bakr initially refused saying "Do you wish me to do something that wasn't done during the Prophets time?" But he later took the advice and a sahaabi named Zaid bin Thabit was designated to write the Quran down and the chapters were arranged by size from long to short.
