The history of the entire Empire is a pretty sprawling topic so it's hard to find a whole history in one book. The ones that exist tend to be extremely long:

Warren Treadgold, A History of the Byzantine State and Society (Stanford University Press, 1997) covers the whole empire, but it's about 1000 pages!

Robert Browning, The Byzantine Empire (Catholic University of America Press, 1980, rev. ed., 1992) is relatively short compared to Treadgold. Probably a better introduction in general.

There are also two classics:

A.A. Vasiliev, History of the Byzantine Empire (University of Wisconsin Press, 1952) and

George Ostrogorsky, History of the Byzantine State, trans. Joan Hussey (Blackwell, 1968)

They're now quite old and out of date, but still a good introduction.

Otherwise, there are tons of books about more specific topics, so if you're interested in a particular time period/geographical area, or a certain subject (society, economy, military, religion, etc), we might be able to recommend something else for you.