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 200s 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 300s AD, and even after that.
Philosophy and Science in Ancient Greece: The Pursuit of Knowledge, by Don Nardo (2004). For teenagers. Don Nardo has written many books for young people about the ancient Greeks.
The Cambridge Companion to Greek and Roman Philosophy, edited by David Sedley (1997).