- Byzantine Armies, AD 1118-1461 (by Ian Heath, Illustrated by Angus McBridge): Part of Osprey's Men-at-Arms series, I picked this one because it corresponds to my particular focus in Constantinople (c. 1150). There is not a lot of depth, but there is a lot of useful gaming info here and the illustrations are great.
- Constantinople: Capital of Byzantium (by Jonathan Harris): If I could only read one book on Constantinople, this would be it.
- The Digest of Roman Law (by Justinian I): Player characters in trouble with the law? Perish the thought! Here are excerpts from Justinian's codification of Roman law. The introductory material, by C.F. Kolbert, is worth the price of the book and is very useful to gamers.
- The Oxford History of Byzantium (edited by Cyril Mango): The title is a bit misleading (which is true of many volumes in the Oxford History series). It is not a typical history book; rather it is a collection of essays on Byzantium. I wouldn't start here but if you already know a bit about Byzantium, some of the essays can be mined for gaming goodies (particularly the religion articles).
- What Life Was Like Amid Splendor and Intrigue: Byzantine Empire AD 330-1453 (edited by Ellen Anker): A lavishly illustrated book that is part of Time-Life's What Life Was Like series, this is a great place to get a feel for Byzantine history and daily life.
If you are looking for an easy-to-read book on Byzantine history as a starting point, I would recommend A Short History of Byzantium by Julius Norwich (just don't cite it in your doctoral dissertation). I also liked Sailing from Byzantium: How a Lost Empire Shaped the World by Colin Wells and Byzantium: The Surprising Life of a Medieval Empire by Judith Herrin. Both books are fun reads.
Steve Jackson Games has a groovy online bibliography of Constantinople and you can purchase their GURPS Hot Spots: Constantinople, 527-1204 A.D. as a PDF.