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.
Quran as a book
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.
