The Quran was revealed to Muhammad (pbuh) who was brought up as an illiterate in an uneducated society. Therefore, when he became the Prophet, he paid special attention to guarding the revelations and spreading them to others. The order followed that he would first learn them by heart and then transmit them to other people around him. The following verse exemplifies this:
“It is He Who has sent amongst the unlettered a messenger from among themselves, to rehearse to them His Signs, to purify them, and to instruct them in the Book and Wisdom,- although they had been, before, in manifest error.” (Al-Jumuah, 62:2)
The Messenger of God was very determined to memorize and protect the revelations that came to him. He was so concerned about forgetting the revelations brought to him by the angel Gabriel that he was acting with haste and immediately moving his tongue. This difficulty for the Prophet was ended by the following commands of Allah:
“Do not move your tongue with it to make haste with it, surely on Us (devolves) the collecting of it and the reciting of it. Therefore when We have recited it, follow its recitation. Again on Us (devolves) the explaining of it.” (Al-Qiyamah, 75:16-19)
“Supremely exalted is therefore Allah, the King, the Truth, and do not make haste with the Quran before its revelation is made complete to you and say: O my Lord! Increase me in knowledge.” (Al-Taha, 20:114)
Thus, the Prophet was learning the revelations by heart splendidly and conveying it to other people in the form that Allah commanded. He was enriching his prayers and revitalizing nights reciting them. Moreover, once a year, he was reciting all the revelations that had come until then with the angel Gabriel. That happened twice in the year the Prophet passed away. The following narration from Aisha and Fatima proves this:
“The angel Gabriel is reciting the Quran once every year. This year that happened twice. So I feel that my decease is soon.”
The Prophet had the Quran written down from the very beginning of Islam. As a matter of fact, the Quran conveys to us the oppositions of the infidels in Mecca in the following manner:
“And they say: The stories of the ancients-- he has got them written-- so these are read out to him morning and evening.” (Al-Maidah, 5:25)
In addition, the following verses point out that the Quran had been written down on paper since the beginning:
“In the Book well-guarded, Which none shall touch but those who are clean.” (Al-Waqiah, 56:78-79)
“In honored books, exalted, purified, in the hands of scribes, noble, virtuous.” (Al-Abasa, 80:13-16)
Furthermore, the occasion that lead Umar to be a Muslim also reveals that the revelations had been written since the first day.
The Messenger of God was memorizing the revelation brought to him by the angel, and then he would call one of the revelation clerks and have him write the revelation indicating which sura (chapter) it belonged to. The revelation clerk would write the revelations down on materials used in those days such as scraps of leather, branches of date trees, flat stones, wood tablets, and blade bones of sheep and camel. As reported in the traditions of the Prophet (hadith), after having a clerk write down a revelation, the Prophet would ask him to read it aloud to make sure it was correctly recorded. Then, the companions would make copies of those properly written texts and secured them for themselves.
In fact although the text was the same as what the Prophet had written down, the Quran did not have its current form or appearance in the period of the Prophet. It was not a book with a hard cover because it was revealed to the Prophet in pieces, as a sura, in verses or even as a part of a verse. The Prophet was teaching every revelation to the companions around him and passing them on to other people who did not directly hear it from himself. In this period, everyone was eagerly waiting for revelations. Upon their arrival, they were acting immediately to learn them. Even the enemies of the Prophet could not stay negligent of the Quran; most of the time, they wanted to listen to the recitation of the Quran either to find out its weaknesses to attack and fight against it or to satisfy their literary tastes with it. So it is not difficult to imagine the greatness of the meanings that the Quran brings to Muslims. The Quran is the nourishment of spirits, the essentials of morality, the basics of prayer, the means for spreading the word of God and the daily remembrance of Him. Simply put, it contains basic rules that order all aspects of human life.
source: last prophet