One of the oldest manuscripts of Quran is believed to be the Uthmani Manuscript which is kept at the Topkapi Palace Museum in Istanbul, Turkey.
During the Caliphate of Usman (ra) he commissioned a committee to compile the parts of Quran in the form of a single book, previously the Surahs and verses of Quran were only available in parts.
Then he sent these copies to different parts of the Muslim world which stretched on 3 continents. The reason behind it was to avoid any mistake in Quran. So if anyone wanted to correct his manuscript of Quran he only had to visit the major cities with official manuscript.
There is another manuscript which is kept at Hast Imam Library in Tashkent, Uzbekistan which is also believed to be an early manuscript of Quran. Though it is not confirmed whether it is from the era of Uthman (Ra) but is believed to be among the oldest manuscript.