One of the things i found of interest is the way Greenblatt scuppers the notion that the Great Library was destroyed by Caliph Omar. But by the time that happened{if indeed it did happen--it might simply be negative propaganda} little of the Great Library was left.
Still Greenblatt provides what is undoubtedly a reasonably accurate outline of events but does perhaps over-simplify things by linking the Library's destruction to the horrifying and brutal murder of Hypatia. The Great Library was most likely destroyed by a multitude of wounds. If any would like to read a very thorough description of it, there is a very well researched article by Heather Phillips in
Library Philosophy and Practice 2010 here:
http://www.webpages.uidaho.edu/~mbolin/phillips.htm
Another interesting article by Brian Haughton outlines what is known about the Great Library:
http://www.ancient.eu.com/article/207/