You could look at:

• the Goths and their influence on both the politics and theology (esp. Arianism) of the Empire
• the role of the bureaucracy
• how the political struggles between the Empire and the West affected ecclesiastical struggles/conflicts (esp. important in Illyricum)
• Justinian's attempts to recapture the West
• The Codex Iustianus and its influence (or lack thereof) on modern/classical Western jurisprudence
• Basil II as the height of the Empire

Do yourself a favor and get Ostrogorsky'sHistory of teh Byzantine Empire. It is fabulous. Also very good is J.B. Bury's History of the Late Roman Empire

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Fredrick T. Greco
Senior Pastor, Christ Church PCA (Katy, TX)
Christ Church Blog

"The heart is the main thing in true religion...It is the hinge and turning-point in the condition of man's soul. If the heart is alive to God and quickened by the Spirit, the man is a living Christian. If the heart is dead and has not the Spirit, the man is dead before God." (J.C. Ryle)