This is a huge book but in my view for non-professionals who are interested to know more about Byzantine Empire it is a very good and complete intro.
It covers both its political history and to some degree its social aspects, especially its religious history. In fact, it is hard to find any other country where the nuanced religious questions mattered so much for the society as they did in Byzantium.
While Byzantium as a state disappeared in 15th century, the question remains which country "inherited" its ideas? Greece, Turkey or Russia, other?
It is interesting to note here that Turkish Ottoman Empire covered almost exactly the same territory as the Byzantium did at its height.
posted by David