[Alexios I, 11th century, source: Wikimedia Commons]
[Coin with the image of Christ on one side and Eirene Doukaina on the other, 11th or 12th century, Classical Numismatic Group, source: Wikimedia Commons]
She was born the eldest child of Emperor Alexios I Komnenos and Irene Doukaina. Anna was highly educated, having studied literature, rhetoric, history, various sciences, and more with the encouragement of her parents.** It is entirely possible that she was able to quote Homer and the Bible from memory when writing the Alexiad.
In 1097 she married Nikephoros Bryennios the Younger, a general, historian, and nobleman. The couple eventually had four children together. Sometime after her marriage, her father put her in charge of the biggest hospital in Constantinople. Not only was she a very successful administrator, but she was apparently also a very good physician and eventually became an expert on gout.
As the eldest child of the Emperor, she may have felt entitled to the throne. At the very least it’s clear that she felt her eldest brother (John, four years younger than she) was not a good ruler. Her mother agreed and supported Anna and Nikephoros in opposition to her son John. It is likely that Anna was involved in a plot to murder her brother at their father’s funeral in 1118.*** The plan was discovered and John forced his sister to retire from politics.
In 1137 Nikephoros died, leaving Anna to retire to a monastery. She undertook to complete the history her husband had started (possibly only barely, considering the work is now attributed entirely to her), calling the finished work the Alexiad. Her brother may have kept the throne, but it is through her eyes that he is remembered and he measures up poorly to her father.
*The date of her death is actually unknown, though 1153 is the most common date given. At the very least, she was still alive in 1148.
**Georgios Tornikes claimed in his funeral oration for her that she had to study some things in secret to avoid facing her parents’ disapproval for studying things considered “dangerous.” Anna Komnene herself, however, neither said nor implied anything of the sort in any of her works. Given that, Tornikes’ claim seems possible, but unlikely.
***There is some debate over whether her husband Nikephoros was involved as well.
Windsor, Laura Lynn. "Anna Comnena." In Women in Medicine: An Encyclopedia, edited by Laura Lynn Windsor, 45-46. Santa Barbara, CA: ABC-CLIO, 2002. [Link to Google Books]
Tyerman, Christopher. Introduction to Chronicles of the First Crusade, translated by Christopher Tyerman, xv-xxxii. London: Penguin Classics, 2004.
Anna Comnena: The Alexiad - Internet History Sourcebooks Project
Anna Komnene - Wikipedia
Anna Comnena - Women in World History
Anna Comnena - Catholic Encyclopedia