Ancient Greece consisted of several hundred relatively independent city-states (polis).
Initial Political institutions: Aristocratic Oligarchies
Many Greek city-states initially started as petty kingdoms.
These petty kingdoms usually has city official who carry out ceremonial functions of the king
However, by 650 BC these petty kingdoms evolved into aristocratic oligarchies. It is unclear how this evolution happened.
Athens is a good example of this evolution.
Athens started as petty kingdom. By 1050 BC, the king had been reduced to a hereditary, lifelong chief magistracy.
By 753 BC, this chief magistracy was reduced to elected chief magistracy, who ruled for 10 years.
Finally by 683 BC, election of chief magistracy, which was a once in decade event became annual affair.
Each stage of this evolution transferred more power to aristocracy at the expense of king.
However this system has one downside. Accumulation of power by small groups of families caused social unrest in many city-states.
Sometimes, due to these unrest, strongmen (powerful person) would seize control and govern the city-states on populist agenda. This would help him to retain power for many years.
Evolution to new Political institutions: Democracy
Athens fell under a control of strongmen or tyrant in the second half of the 6th century.
When Athenian regained control of the city from this tyrant they wanted a radical solution to prevent aristocracy or tyrant from regaining power.
The unique solution to this problem was democracy. Thus Athenians founded the world’s first democracy.
By 621 BC, all citizen of Athens were permitted to attend citizens’ assembly. Within 20 years, all citizens except the poorest citizens could address the assembly or run for office.
All citizens has equal privileges in the assembly. However, foreigners or slaves were considered non-citizens who had no political rights at all.
Soon, at least fifty-two classical Greek city-states including Corinth, Megara, and Syracuse also had democratic regimes during part of their history.
Not all city-states changed their political institutions to democracy, instead some of them retained more traditional forms of government.
Spartan Exceptionalism: Kings and Council of elders
As in many other things, Sparta was a notable exception. They were ruled by not one but two hereditary kings (Agiads and the Eurypontids). The founders of both dynasties were believed to be twin sons of Aristodemus, a Heraclid ruler.
However the power of king was not absolute. Their power was kept in touch by a council of elders and magistrates specifically appointed to watch over the kings.