"Byzantine civilisation" by Steven Runciman could the thing you need. Try also "Cambridge Medieval History", vol IV or anything by Bury. If, by any chance, you have a translation of "History of Byzantine" by Georgie Ostrogorski, I strongly recommend it.
Enjoy your ortodox version of Medieval Christianity
P.S. I've forgotten to mention a french author, Paul Lemmer (I think this is the write spelling). He wrote the shortest
summary of the Byzantine history, but it is also a very good one.