[Lonesome in Massachussets]

It is not at all clear how much destruction of the library can be attributed to Ceasar and even his critics grant that any damage was incidental to burning the Egyptian Navy of Ptolemy XIII. The Library and adjoining buildings were clearly open for business almost immediately after the siege in 48 BC and for centuries later. The library survived at least until the time of the Caliphate, but did not survive it. One story has it that when Caliph Omar’s General Amr asked for instructions on what to do with the library Omar wrote back, “If those books are in agreement with the Quran, we have no need of them; and if these are opposed to the Quran they are heresy, therefore destroy them all.”

[SunkenCiv]

Right. There's a persistent myth that Caesar burned the library, but since it is known to have continued to exist thereafter, and the line that describes the event cites "some books which chanced to be there". The library was known as "the ships' library" because its founder had ships in the very busy port searched, any books found removed and copied, and the copies taken back to the ship, with the original archived.