Ancient Greece spans hundreds of years of history starting at about 800 BC. Ancient Greece is unique in many respects. First of all, it is the first period with historiography. This means it is the first time-period about which we have historical accounts written by people who lived back then. Herodotus, born in present-day Turkey in the 400s BC, is considered the father of history.
The Greece of the past is not how we know it today. First off, it wasn't a united country. Instead, it was made up of hundreds of city-states and tribes in what is now Greece and Turkey. A city-state is a city, and the lands that surround it, which functions as an independent nation. They shared common languages, and a similar culture, but were not all ruled over by one king or system of government. Some city-states included Corinth, which was the richest, and Thebes, where legends say Hercules was born.
Warring and feuds between the city-states were very common. The most famous of these city-states are Athens and Sparta, which were bitter rivals, and fought the Peloponnesian War.
Sparta was the most militarily powerful of the city-states beginning in 650 BC. This was because of its unique system of government which was focused entirely on the military. Male Spartan citizens were taken from their parents at an extremely young age and trained rigorously. They were expected to serve in the army until they were 60 years old. This left female Spartan citizens in charge of households, giving them more rights than women in other parts of the world during this time. The rest of the population were either freedmen, responsible for trade, or slaves, who worked the fields to feed the army.
Athens, in turn, was the most populous city-state at over 360,000 people in 431 BC. It was the intellectual capital of the region, famed for its temples, arts, and theatres. During the period, it was a great center of learning, and many of the famous philosophers we know today lived here, including Aristotle, Plato, and Socrates. Though it was first ruled by kings, Athens was the site of the first democratic government in the world in 510 BC.
Athens' independence ended when Phillip II of Macedon, the father of Alexander the Great, conquered them. Alexander is of course well-known today. His story is long and complicated, but he is most famous for forming the largest land empire in history up to that point, stretching from his hometown in Greece all the way to India. However, he failed to set up mechanisms which would keep it alive after his death. In fact, when asked which of his generals the empire's rule should fall to when he died, he replied 'to the strongest.' This of course resulted in a breaking up of the empire.
Though today the wartime exploits of Sparta and Alexander the Great are celebrated in films and other forms of media, it's the intellectual pursuits of the Athenians who have made the greatest mark on the modern world. Athens, as the birthplace of democracy, laid the foundation for all that was to follow in the Western world for the next two thousand years.