The cause of the Persian War was the Ionian Revolt. The Persians had a lot of territories and wanted to expand, but so did the Athenians. They wound up expanding into each other, causing a land dispute.
The Battle of Marathon was fought by the Spartans and the Athenians, against the Persians in 490 BC. Persia had 25,000 soldiers and Greece only 10,000. When the Persians arrived at the shore, the Greeks raced to them and slaughtered the entire army before they were set up.
Aaaahhh! They weren't supposed to attack until tomorrow! We don't have a plan!
In the battle of Thermopylae, the Persians brought 100,000 soldiers, compared to the Spartans 300; lead by King Leonidas. The Spartan's fought hard, but lost after a Greek traitor told them about an alternate route around the mountain.
This is a Greek trireme. A trireme is a smaller, lighter ship with a hard pointed bow, used to plow into other boats.
At the battle of Salamis, Xerxes sailed to Athens in 478 BC, only to find it deserted. The Athenian army had sailed to Salamis and was waiting to attack by sea. Although the Greeks had fewer ships their, ships were smaller, faster, and more manuervable, and the Persians were quickly defeated.
The final battle of the Persian War, the battle of Platea, was fought on land in the year 479 BC. The Greeks won but after the war Greece more divided than united.
After the Persian War ended Athens created the Delian League, a group of soldiers trained to protect Greece from possible invaders. The creation of this group is what will lay the foundation of the Peloponnesian War.