The Dynamics of Ancient Empires is a fantastic choice. Ian Morris' section on the Athenian "Empire" is a classic, and there are also interesting treatments by other contributors like Scheidel.

I second the recommendation of The Dynamics of Ancient Empires, which is the best overview I've come across.

Ancient Empires: From Mesopotamia to the Rise of Islam by Mark Graham and Eric Cline is another decent introduction to ancient empires.