Ancient Greek philosophy is dominated by three very famous men: Socrates, Plato, and Aristotle. All three of these lived in Athens for most of their lives, and they knew each other. Socrates came first, and Plato was his student, around 400 BC. Socrates was killed in 399 BC, and Plato began his work by writing down what Socrates had taught, and then continued by writing down his own ideas and opening a school. Aristotle, who was younger, came to study at Plato's school, and ended up starting his own school as well.

In the years after Plato and Aristotle died, in the 200's BC, three famous kinds of philosophy started up in the schools  that Plato and Aristotle had started. These are the Stoics, the Skeptics, and the Epicureans. Each of these continued to be important ways of thinking about the world all the way through the Roman Empire, until people converted to Christianity in the 300's AD, and even after that.

Greek women wore one large piece of wool or linen, wrapped around them and pinned in various ways  to make it stay. The ways of pinning it changed over time. One way was to fold the cloth in half, and put it so that the fold in the cloth came under your right armpit and down your right side. Then pull up on the front and  the back of the cloth so they meet over your right shoulder and pin the front and the back together with a big safety pin. Then pull more of the front up over your left shoulder, and pin it to the back in the same way. Finally you will notice that your dress is still open all along your left side: tie a belt around your dress at the waist to keep your dress closed. These dresses always came down to their ankles.

Aristotle divided Greek governments into monarchies, oligarchies, tyrannies and democracies, and most historians still use these same divisions.  For the most part, Greece began by having monarchies, then oligarchies, then tyrannies and then democracies, but at each period there were plenty of city-states using a different system, and there were many which never did become democracies or tyrannies at all.

In the Late Bronze Age (the Mycenean period), between about 2000 and 1200 BC, all Greek city-states seem to have been monarchies, ruled by kings. Homer's Iliad, and Greek mythology in general, shows us a whole series of kings like Agamemnon and Theseus, and some of their palaces have survived for archaeologists to dig up.

After the Dark Age, though, only a few Greek city-states still had kings. Sparta is the most famous of these, though actually Sparta had two kings, usually brothers or cousins, at the same time. One would stay home and the other go off to fight wars.
Most city-states in the Archaic period were ruled by oligarchies, which is a group of aristocrats (rich men) who tell everyone else what to do. Then in the 600's and 500's BC a lot of city-states were taken over by tyrants. Tyrants were usually one of the aristocrats who got power over the others by getting the support of the poor people. They ruled kindof like kings, but without any legal right to rule.

In 510 BC, the city-state of Athens created the first democratic government, and soon other Greek city-states imitated them. Even city-states that weren't Greek, like Carthage and Rome, experimented with giving the poor people more power at this time. But Athenian democracy did not really give power to everyone. Most of the people in Athens couldn't vote - no women, no slaves, no foreigners (even Greeks from other city-states), no children. And also, Athens at this time had an empire, ruling over many other Greek city-states, and none of those people living in the other city-states could vote either. Of course it is a lot easier to have a democratic government when you are only deciding what other people should do.

(And many Greek city-states kept oligarchic government, or tyrannies, or monarchies, through this whole time).

Then in the 300's BC, Greece was conquered by Philip of Macedon, and all of Greece began to be ruled by him as their king (in theory he was only leading a league of Greek city-states, but really he acted like a king). Athens and other Greek city-states still kept their local democracies or oligarchies for local government, but bigger decisions were made by Philip, and then by Philip's son Alexander the Great.

After Alexander died in 323 BC, Greece became a kingdom ruled by a series of Macedonian kings, until it was gradually taken over by the Romans between 200 and 146 BC. From 146 BC on, Greece was a province of the Roman Empire. Even after the Roman Empire in the West collapsed, Greece was still part of the Eastern Empire. In the 1100's and 1200's AD, parts of Greece were taken over by Normans, who built castles and ruled as kings.

And finally, in 1453 AD, the Turks took over and established Greece as a province in their Ottoman Empire; there was little change in the system of government from the Roman Empire. 

The Greeks were very interested in science as a way of organizing the world and making order out of chaos, and having power over some very powerful things like oceans and weather. From about 600 BC, a lot of Greek men spent time observing the planets and the sun and trying to figure out how astronomy worked. They must have gotten their first lessons from the Babylonians, who were very good at astronomy and also very interested in it.
By the 400's BC, Pythagoras was interested in finding the patterns and rules in mathematics and music, and invented the idea of a mathematical proof. Although Greek women usually were not allowed to study science, Pythagoras did have some women among his students. Socrates, a little bit later, developed logical methods for deciding whether something was true or not.
In the 300's BC, Aristotle and other philosophers at the Lyceum and the Academy in Athens worked on observing plants and animals, and organizing the different kinds of plants and animals into types. Again, this is a way of creating order out of chaos.

The Greeks took games of all kinds very seriously, but especially physical athletic competition. The Greeks believed that their gods particularly loved to see strong, fit, graceful human bodies, especially boys' and men's bodies. So one way to get on the good side of the gods was to exercise, to eat right, to oil your skin, to create a beautiful body that the gods would love. Because of the Greek tendency to turn everything into an agon, a competition, this also meant that there were a lot of athletic competitions in Greece. The most famous of these is the Olympic Games, but there were other games held in other places as well, like the Isthmian Games at Corinth.