Athens was no exception. A class of aristocrats ruled the city and excluded the wealthy nouveaux riches. Moreover, there were social conflicts. One would have expected the rise of tyrant, but instead the Athenians appointed a wise man named Solon as lawgiver (594/593).
He is responsible for several measures: for example, he decreed that no Athenian would be sold into slavery, even if he were severely indebted (a hectemoros), and that magistracies were open to all rich people (diminishing the power of the aristocrats). He also took economic measures and founded the Heliaia, the people's court. The main result was that people for the first time began to define themselves as Athenians.
After Solon had written these laws, he left Athens for some time. He is said to have visited Egypt and king Croesus of Lydia. Later, he returned home, where he was forced to see how Athens got its tyrant: Pisistratus.
Solon is reckoned among the Seven sages.
Plutarch's Life of Solon is available at LacusCurtius