For background reading on the history of Byzantium, you might consider:
- Byzantium by Giles Morgan, for a brief, yet comprehensive one-volume history.
- A Short History of Byzantium by John Julius Norwich, for a one-volume version of his 3-volume work.
- Byzantium: The Decline and Fall, volume 3 of Norwich's complete history for the period covering Alexius and Anna Comnena.
- Sailing from Byzantium: How a Lost Empire Shaped the World by Colin Wells on the lasting influence of Byzantium.
Finally, if you're curious how the life of Anna Comnena inspired a young-adult novel, try: Anna of Byzantium by Tracy Barrett.