The world's first known empires took shape in Mesopotamia between the eastern shores of the Mediterranean Sea and the Persian Gulf, beginning around 2350 BCE. The next 2,500 years witnessed sustained imperial growth, bringing a growing share of humanity under the control of ever-fewer states. Two thousand years ago, just four major powers--the Roman, Parthian, Kushan, and Han empires--ruled perhaps two-thirds of the earth's entire population. Yet despite empires' prominence in the early history of civilization, there have been surprisingly few attempts to study the dynamics of ancient empires...