The Pelopennesian War, a war that started because of two allies fighting each other, both the City States of Corinth and Megara are having a conflict, they were allies of Athens, their alliance was called the Delian League, Athens sided with Megara, despite being allies with both of them, and Corinth sided with Sparta and his allies, which is called The Peloponnesian League.
The First part of the War is called The Archidamian War, which where the Spartans launch attacks on Attica, while Athens Launch attacks at various points in the Pelopennesian League, then these Spartans got the (pretty bad) idea of invading Syracuse, so they ask "Why not?", they then launched an attack to Syracuse, which failed, this is often called the second part of the war. The Third Phase, named the Ionian or Decelean War began, The Spartans attack the little village of Decelea, which was a strategic point in Greece, they succeeded, mostly because of Persians, they helped the Spartans win.