The Peloponnesian Wars.
If I understand the question correctly, it was The Peloponnesian War from 431 to 404 BC that Athens and Sparta fought each other. Sparta was the victor.
Athens and Sparta did not fight each other in isolation. They fought as allies and as adversaries in various conflicts over a couple of hundred years. So Athens did not defeat Sparta or Sparta defeat Athens. They were involved in wider conflicts in the battles.
There was not rivalry. Sparta, although militarily powerful, was usually reluctant to go to war. Athens, overconfident with the power it gained from its empire, was aggressive and interfered in the affairs of other cities. Sparta appealed to Sparta to back off when it tried to bankrupt Megara, a member of the Peloponnesian League, A rampant Athens persisted and war ensued.
Athens formed the Delian League with other city states including Sparta
You are obviously asking about ancient Athens. Well, during the years there were different allies to Athens according to what the needs required. At some point it could have been Sparta and then at another they were one against the other. Anyway, Sparta was mostly allied to Athens when it comes to matters of being commonlt threaten. Thebes and Megara were also traditional allies on account of being close to Athens. Boetians and Corinthians too for the same reason.
in the pelopponesian war
they had fought together and against each other
Each other. Athens and Sparta, with their respective Greek allies, fought each other. The Persian Empire later sided with Sparta against Athens, but mostly it was Greek against Greek.
If I understand the question correctly, it was The Peloponnesian War from 431 to 404 BC that Athens and Sparta fought each other. Sparta was the victor.
The city-states of Athens and Sparta fought each other in the Peloponnesian War .
The war was fought between Athens and Sparta, but both cities had many allies in other parts of Greece, some of whom were forced to fight. Toward the end of the war, Sparta allied with an old enemy, the Persian Empire, against Athens.
peloponnesian war
The city states of Athens and Sparta and their allies fought each other in the Peloponnesian War .
Peloponnesian War
Persian Wars
Athens and its allies and Sparta and its allies.
Athens and Sparta did not fight each other in isolation. They fought as allies and as adversaries in various conflicts over a couple of hundred years. So Athens did not defeat Sparta or Sparta defeat Athens. They were involved in wider conflicts in the battles.