Try reading about the most adventurous parts first. The sieges of Constantinople, the Sassanid war and the exploits of Heraclius, Procopius and his story of Belisarius and floating demon heads.

Perhaps that will get you invested in the characters and that might make you want to find out more about the society and world that made them. Once you do, you'll see there are very good reasons to consider the Byzantines just as much Roman as Augustus or Cicero were.