OnIslam.net

The revelation contained in the Qur'an has been transmitted to us by numerous persons in two ways: orally and in written form. 

Oral transmission of the revelation was based on hifz or memorization. Prophet Muhammad himself was the first to commit a revelation to memory after the Angel Gabriel had brought it to him:

{Move not thy tongue concerning the (Qur'an) to make haste therewith. It is for Us to collect it and promulgate it; but when We have promulgated it, follow thou its recital} (Al-Qiyamah 75: 16-19)

{... a Messenger from God, reciting scriptures, kept pure and holy} (Al-Bayinah 98: 2)

Memorization by the Companions 

The Prophet (peace and blessings be upon him) then declared the revelation and instructed his Companions to memorize it. The case of Ibn Mas`ud, who was the first man to publicly recite the Qur'an in Makkah, shows that even in the very early phase of the Islamic ummah, recital of the revelation from memory was practiced by the Companions:

The first man to speak the Qur'an loudly in Makkah after the Prophet was `Abdullah ibn Mas`ud. The Prophet's Companions came together and mentioned that the Quraish had never heard the Qur'an distinctly read to them ... When (Ibn Mas`ud) arrived at the maqam, he read "In the name of God the Compassionate the Merciful", raising his voice as he did so. (he continued,) {The Com- passionate who taught the Qur'an ...} (Ar-Rahman 55:1-2) They got up and began to hit him in the face; but he continued to read so far as God willed that he should read. (Ibn Hisham, Sirat An-nabi, Cairo, n.d., 1, p.206.)

It is also reported that Abu Bakr used to recite the Qur'an publicly in front of his house in Makkah. (Ibn Hisham)

The Prophet encourages memorization 

There are numerous ahadith, giving account of various efforts made and measures taken by the Prophet to ensure that the revelation was preserved in the memory of his Companions. The following is perhaps the most clear:

Narrated `Uthman ibn `Affan: The Prophet (peace and blessings be upon him) said: "The most superior among you (Muslims) are those who learn the Qur'an and teach it." (Bukhari)

It is also well known that the recital of the Qur'an during the daily prayers is required and hence many Companions heard repeatedly passages from the revelation, memorized them and used them in prayer.

The Prophet also listened to the recitation of the Qur'an by the Companions:

Narrated `Abdullah ibn Mas`ud: Allah's Messenger said to me: "Recite (of the Qur'an) for me". I said: "Shall I recite it to you although it had been revealed to you?!" He said: "I like to hear (the Qur'an) from others". So I recited Surat An-Nisa' till I reached: {How (will it be) then when We bring from each nation a witness and We bring you (O Muhammad) as a witness against these people?} (An-Nisa’ 4: 41). Then he said: "Stop!" I saw his eyes were shedding tears then. (Bukhari)

The Prophet sent teachers to communities in other places so that they might receive instruction in Islam and the Qur'an. The case of Mus`ab bin `Umair illustrates that this was so even before the hijrah:

When these men (of the first pledge of `Aqaba) left (for Madinah) the apostle sent with them Mus`ab ibn `Umair... and instructed him to read the Qur'an to them and to teach them Islam and to give them instruction about religion. In Madinah, Mus`ab was called ‘the reader’. (Ibn Hisham, p. 199.)

Another well-known case concerns Mu`adh ibn Jabal who was sent to Yemen to instruct the people there.

Qur'an readers among the Companions 

As-Suyuti in his Al-Itqan mentions more than twenty well-known persons who memorized the revelation, among them were Abu Bakr, `Umar, `Uthman, `Ali, Ibn Mas`ud, Abu Hurairah, `Abdullah ibn `Abbas, `Abdullah ibn `Amr ibn Al-`As, `A'ishah, Hafsah, and Umm Salamah (may Allah be pleased with the all).

From among these, the Prophet himself recommended especially the following:

Narrated Masruq: `Abdullah ibn `Amr mentioned `Abdullah bin Mas`ud and said: I shall ever love that man for I heard the Prophet saying: Take (learn) the Qur'an from four: `Abdullah ibn Mas`ud, Salim, Mu`adh and Ubay ibn Ka`b. (Bukhari)

Another hadith informs us about those Companions who had memorized the Qur'an in its entirety and gone over it with the Prophet before his death:

Narrated Qatada: I asked Anas ibn Malik: Who collected the Qur'an at the time of the Prophet? He replied, Four, all of whom were from the Ansar: Ubay ibn Ka`b, Mu`adh ibn Jabal, Zaid ibn Thabit and Abu Zaid. (Bukhari)

The fact that some of the earliest historical reports make special mention in the accounts of the battles that were fought, of Muslims killed who knew (something of) the Qur'an by heart, gives a clear indication that memorization of the revelation was considered important and widely practiced from the earliest times.

It is therefore certain that the Qur'an had been memorized by the Companions of the Prophet during his lifetime. This tradition continued among the Companions after the Prophet's death and, later, among the tabi`un (the Companions' successors) and all generations of Muslims that have followed, until today.