Wars were very common in ancient Greece. The Greeks lived in little city-states, each one like a small town in the United States today, with no more than about 100,000 people in each city-state. These city-states - Athens, Sparta, Corinth, Thebes - were always fighting each other over their borders. Often they would get together in leagues, a lot of city-states together, to fight as allies.
Sometimes other people invaded Greece, and then there would be wars to defend the city-states from the invaders. Sometimes the city-states fought together, and sometimes they didn't. Then again, sometimes the Greeks fought in other countries. They invaded other countries and took them over, or they raided other cities and took their stuff. And they often fought for pay, as mercenaries, when one foreign country fought another. Although there were many wars in ancient Greece, most of them we don't know very much about.
There are four main wars that we do know about, thanks to the writing of Homer and Herodotus and Thucydides and Arrian. These are the Trojan War (about 1250 BC, which could be a legend), the Persian Wars (490-480 BC) and the Peloponnesian War (441-404 BC) and the campaigns of Alexander the Great (331-323 BC). Then a little later, Greece was taken over by the Romans (146 BC), which we know about thanks to Polybius.
About 650 BC, Greek generals in various different city-states came up with a new way of fighting battles that gave Greek soldiers of the Archaic period a big advantage over the soldiers of other countries like Egypt or the Lydians. Instead of fighting all in a big crowd, running forward and just trying to get at the enemy any which way, Greek generals trained their soldiers to fight in lines, shoulder to shoulder. In this way each man (women were not allowed to be soldiers) was protected by the shield of the man standing next to him. When they all marched forward together, no enemy spears or arrows could get through their wall of shields.
A soldier who fought this way was called a hoplite, and a group of soldiers who fought this way were called a hoplite phalanx. A hoplite phalanx was a very strong military formation - but it only worked if all the soldiers were well trained, and if they were all brave enough to hold the line. If anyone started to run away, the whole line would fall apart, and it wouldn't work. Or, if some men went slower than others, or got out of step, it wouldn't work. So hoplites needed to spend a lot of time training, the way people today train to be in a marching band, for instance.