The End of Sparta
In 441 BC, the Spartans decided that the Athenians were pushing everybody around too much, and they got an alliance of other city-states together (mainly Corinth) and attacked Athens to break up Athenian power. This is known as the Peloponnesian War, because Sparta is in the part of Greece called the Peloponnese.
At first the Spartans were losing the war, but then when there was a plague in Athens they began to win. They won even more after they got advice from an Athenian called Alcibiades. He told them to build a navy. In the end, the Spartans won the Peloponnesian War. In 404 BC, they took over Athens and destroyed the fortification walls around Athens.
But the Spartans didn't get to enjoy their victory for very long. In 369 BC, the Theban army came down into the Peloponnese and helped the Messenians (the helots) get free of the Spartans and form their own city-state. After this, the Spartan men had to work on farms to feed themselves and their children, and they couldn't train all the time. So they weren't the best army anymore, and Sparta became just another small town, without much power.
By 338 BC, Sparta had been taken over by Philip of Macedon, like all the rest of Greece. It never really got to be independent again, but was part of Alexander the Great's empire, then part of the Roman Empire, then the Byzantine Empire, and finally, in 1453 AD, the Ottoman Empire.
Learn by doing: compare freeing the helots to freeing the American slaves
More about Corinth
Leonidas: Hero of Thermopylae, by Ian Macgregor Morris (2003). A biography for young adults.
The Spartan Army (Osprey Military Elite Series, 66), by Nicholas Sekunda and Richard Hook (1998). Easy reading.
The Spartans: The World of the Warrior-Heroes of Ancient Greece, from Utopia to Crisis and Collapse, by Paul Cartledge (2003). This is pretty hard going, but Cartledge knows everything about ancient Sparta.
Spartan Women, by Sarah B. Pomeroy (2002). Pomeroy was one of the first feminist historians to write about women in the ancient world, and she's still one of the best.