Traditional Muslim scholars are of the view that the Qur'ān was preserved both through memorization and in writing as soon as its revelation began. The Prophet (sws) himself would be the first to commit a revelation to memory after archangel Gabriel brought it to him. He would then declare the revelation and instruct his Companions to memorize it. The Qur'ān was memorized by a vast majority of them. This process of memorization remained the primary means of preservation and transmission of the Qur'ān over the centuries.
As far as the written collection of the Qur'ān is concerned, traditional Muslim scholars generally identify three stages: i) collection under the Prophet Muhammad (sws), ii) collection under Abū Bakr (rta), iii) collection under 'Uthmān (rta). Some narratives also mention that the first person to collect the Qur'ān was 'Umar (rta); however, they have been regarded to mean that he was the first person who advised that the Qur'ān be collected. Certain other narratives attribute a Qur'ānic collection to 'Alī (rta). Some Muslim scholars are of the opinion that it refers to memorization, while there are some others who believe that it was a written collection of a personal nature.
During the time of the Prophet (sws), whenever a portion of the Qur'ān was revealed, it was written down by scribes and read out to him to safeguard against any error. This revelation would be written on various writing surfaces which were available at that time like pieces of saddle-wood (aqtāb)), bones (aktāf), leather (adīm), parchment (raqq) as well as on leaves (sa'af), trunks (kirnāf) and bark ('usub) of palm trees. However, till the death of the Prophet (sws), the Qur'ān was not written in book form because there was always a chance of abrogation of some previous verse. So though all of the Qur'ān had been written on various materials, it was not written in one place nor were its sūrahs arranged in their final sequence (ghayra majmū' fī mawdi' wāhid wa lā murattab al-suwar).
In the time of the caliph Abū Bakr (rta), a number of Muslims who had memorized the Qur'ān were killed. It was feared that unless a written copy of the Qur'ān was prepared, a large part of it might be lost. 'Umar (rta) succeeded in convincing Abū Bakr (rta) to initiate this task and Zayd ibn Thābit (rta) was employed for this purpose. Zayd (rta) collected the Qur'ān from various materials on which it had been written and prepared a complete copy. This copy remained with Abū Bakr (rta) till his death, then with 'Umar (rta) till his death and finally it came in the custody of his daughter, Hafsah (rta). Later the Ummayid caliph Marwān ibn al-Hakam (d. 105 AH) had it destroyed thinking that people might start doubting it.
Then in the time of the caliph 'Uthmān (rta), disputes arose among the soldiers of the Syrian and Iraqī armies in reciting the Qur'ān. At that time, they were fighting at the battle fronts of Armenia and Azerbaijan. When 'Uthmān (rta) was informed of this state of affairs by his general Hudhayfah ibn al-Yamān (rta), he borrowed the suhuf kept with Hafsah (rta) which had been prepared in the time of Abū Bakr (rta). He then constituted a committee of four people to prepare copies of these suhuf in the dialect of the Quraysh. Later 'Uthmān (rta) dispatched these copies to important areas of the Muslim empire and collected and destroyed all other masāhif. 'Abdullāh ibn Mas'ūd (rta), who at that time was residing in Kūfah, however refused to hand over his copy of the Qur'ān.
During all this time, memorization of the Qur'ān continued.
Described above is the view of traditional Muslim scholars regarding the collection of the Qur'ān. It may also be noted that they are almost unanimous that the verses within the sūrahs were divinely arranged in the lifetime of the Prophet (sws); however, as far as the sūrahs themselves are concerned, the majority opinion is that they were arranged by the Companions (rta) in the time of 'Uthmān (rta).
Thus according to traditional Muslim scholarship, it was 'Uthmān (rta) who was responsible for a textus receptus ne varietur of the Qur'ān. It was nothing but the Qur'ān revealed to the Prophet (sws) written in the dialect of the Quraysh with the sūrahs arranged in their current form by the Companions (rta).