Athens, another large city-state, was the birthplace of democracy, or the idea that each person could have a voice in what laws were passed and who made up the government. (This, of course, meant each citizen could take part in government. A citizen was a person who was born in Athens and who owned land there. This was nowhere near the majority.)
Early in its history, Athens was ruled by tyrants, some of whom worked to create democracy. The Athenians invented the practice of ostracism to deal with tyrants. Basically, each person could decide to target one person to be kicked out of Athens. If enough people named a person, he would be banished for 10 years. Athens had its own lawgiver (like Lycurgus of Sparta). His name was Solon, and his laws formed the basis for the democracy of Athens
Athens was also a place of great culture. Philosophers like Socrates, Plato, and Aristotle studied and taught in and around Athens. Many of the famous buildings that are only ruins today were in Athens. An example is the Parthenon.
Athens was the home of the Greeks' great fleet, which beat back the invading Persians several times during the Persian Wars. Athens also used this fleet to create an empire. Other, smaller city-states grew afraid of Athens' power and sided with Sparta, another large city-state, in the Peloponnesian War, which ended in the defeat of Athens.
This war left the Greeks so weak from fighting each other that they were easy targets for a determined conqueror like Alexander the Great, who conquered Greece on his way to ruling most of the known world. (He conquered the mighty Persian Empire and won land all the way to India before his untimely death at age 23.)