There were many Greek battles but these are the 3 most important.
The first battle is the Battle of Salamis( it was a sea battle ). The battle was between the Greeks ships and 57,000 crewmen versus the Persians ships and their crew of 140,000 men. The Greeks fled, but when the Persians were lured into to a strait that their ships were to big maneuver through, the Greeks turned back to fight and won the battle. This battle was important because it was the major battle against the Persians at sea.
The second battle is the Siege of Tyre. The Siege had the 70,000 Greeks on one side, and on the other, were 70,000 Tyrians. After seven months the Tyrians desperate resistance was crushed by Alexander and his men, and the city was in Greek hands. This was an important battle because months later, Alexander and his armies took over the Persian empire.
The third battle was the battle of Gaugamela. The battle was fought between 47,000 Greeks, led by Alexander, and 86,000 Persians lead by Darius ( the king of Persia ). The Greeks destroyed every weapon that the Persian forces attacked them with and won the battle. Two months after the battle, Darius died, and Alexander died in Babylon. This battle was important because it was Alexander’s last battle.
All of these battles changed history.