Hegemony, or the concept of one state being dominant over others, has its roots in Ancient Greek history. In fact, it used to refer exclusively to one city-state exerting control over its neighbors. Before reaching common usage in the 1800s, the term was borrowed in the 1560s directly from the Ancient Greek word hegemonia, which stems from hegemon, a word which could mean "leader" or "authority". Ultimately, that is thought to trace to the verb hegeisthai, "to track down" (it had a figurative definition of "to lead") and finally the Proto-Indo-European root sehg, "to seek out" (interestingly, this also is the etymon of the English word sake). Apparently hegemony can be pronounced either with the g sounding like a j or a g in British English, which I didn't know - Americans only say it with a j sound.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.