Where to start reading and researching the Byzantine empire?

We've got a few books on the Booklist but it looks like that section hasn't been updated recently.

For a relatively short overview, there is Robert Browning, The Byzantine Empire (Catholic University of America Press, 1980, rev. ed., 1992).

For a much, much bigger overview, there's Warren Treadgold, A History of the Byzantine State and Society (Stanford University Press, 1997).

Are you looking for any specific topic? There's an incredibly vast amount of books and articles about the Empire in many different languages but if you're looking for a particular period or subject it would help marrow it down.

For the political situation in the 11th-12th centuries, for example, there is Michael Angold, The Byzantine Empire, 1025-1204: A Political History, 2nd ed. (Longman, 1997).

For the military, you could start with John Haldon, Warfare, State, and Society in the Byzantine World, 565-1204 (Routledge, 1999, repr. 2003).

For the Empire's relationship with western Europe during the crusades, try Jonathan Harris, Byzantium and the Crusades (Hambledon and London, 2003).

For economics, see Angeliki E. Laiou, The Economic History of Byzantium: From the Seventh Through the Fifteenth Century (Dumbarton Oaks, 2002).

For questions of how the Byzantines saw themselves, Anthony Kaldellis has some great recent books. See for example Romanland: Ethnicity and Empire in Byzantium (Harvard University Press, 2019).

This is only a very tiny selection though (and kind of skewed toward things I'm interested in, honestly). Let me know if I can help find something more specific.