The Greeks had a lot of different kinds of governments, because there were many different city-states in ancient Greece. Each city-state had their own government. People‘s ideas about what made a good government changed over time, too.
The Greek philosopher Aristotle divided Greek governments into monarchies, oligarchies, tyrannies and democracies, and most historians still use these same categories. Most city-states in Greece started out by having monarchies, then oligarchies, then tyrannies and then democracies, but at each period there were plenty of city-states using a different system, and there were many city-states which never did become democracies or tyrannies at all.
In the Late Bronze Age (the Mycenean period), between about 2000 and 1200 BC, all Greek city-states seem to have been monarchies, ruled by kings. Homer’s Iliad, and Greek mythology in general, shows us a whole series of kings like Agamemnon and Theseus, and some of their palaces have survived for archaeologists to dig up.
After the Dark Age, though, only a few Greek city-states still had kings. Sparta is the most famous of these, though actually Sparta had two kings, usually brothers or cousins, at the same time. One would stay home and the other go off to fight wars.
Most city-states in the Archaic period were ruled by oligarchies, which is a group of aristocrats (rich men) who tell everyone else what to do. Then in the 600s and 500s BC a lot of city-states were taken over by tyrants. Tyrants were usually one of the aristocrats who got power over the others by getting the support of the poor people. They ruled kind of like kings, but without any legal right to rule.
In 510 BC, the city-state of Athens created the first democratic government, and soon other Greek city-states imitated them. City-states that weren’t Greek, like Carthage and Rome, also experimented with giving the poor people more power at this time. But Athenian democracy did not really give power to everyone. Most of the people in Athens couldn’t vote – no women, no slaves, no foreigners (even Greeks from other city-states), no children. And also, Athens at this time had an empire, ruling over many other Greek city-states, and none of those people living in the other city-states could vote either. Of course it is a lot easier to have a democratic government when you are only deciding what other people should do.
Learn by doing: design your own perfect government
More about Greek government
More about Athenian democracy
Oxford First Ancient History, by Roy Burrell and Peter Connolly (1997). Lively interviews and pictures make the ancient Mediterranean come to life. For teens.
Cleisthenes: Founder of Athenian Democracy, by Sarah Parton (2002). A biography of the founder of Athenian democracy.
Athenian Democracy, by A.H.M. Jones (reprinted 1986). One of the great social historians of the 20th century, though this isn’t easy going.
Alternatives to Athens: Varieties of Political Organization and Community in Ancient Greece, a collection of essays edited by Roger Brock and Stephen Hodkinson (2003). Each chapter presents a different kind of Greek government: oligarchies, tyrannies, monarchies, and so on. By specialists, for specialists.
Rome, the Greek World, and the East: Government, Society, and Culture in the Roman Empire, by Fergus Millar, Hannah M. Cotton, and Guy Rogers (2004). Millar is an expert on Roman government. This book deals with how the Romans governed in Greece.
Ottoman Centuries, by Lord Kinross (1979). A short introduction to Ottoman government, for the non-specialist. It’s a little out of date, so it doesn’t consider the role of Islam, or the role of women, as much as it might have.