Ancient Greek philosophy

Ancient Greek philosophy started in the 6th century BC and continued during the Hellenistic period and Roman Empire.
Philosophy is a way to think about the world. The term was invented in Greece. Then it included the natural sciences, maths, politics, and ethics.
Greek philosophy is one of the foundations of Western culture. It has been a basis for thinking in Rome, Islamic philosophy, the Renaissance and the Age of Enlightenment. Greek philosophy may have been somewhat influenced by the ancient Near East.
Some of the most important early philosophers are Socrates, Aristotle, and Plato. Alexander the Great learned Greek philosophy before conquering the Persian Empire.
Many philosophers thought mathematics was important to all knowledge, and Euclid was one of the founders of mathematical thought. He wrote a famous book on geometry now called Euclid's Elements.
Before Socrates
Many sophists were active, including Protagoras. They are known mostly from what Socrates said against them.
Pythagoras may have been a mystic or a rationalist. We do not know that much about him. He is known for the Pythagorean theorem.
Classical Greek philosophy
Socrates
Socrates (c.470-399 BC) may have been born in Athens in the 5th century BC. We only know of him through the writing of Plato and others. Athens was a center of learning. People went there to talk about ideas.
However, their criticism of the elite had consequences. Athens was an important city and, naturally, it had significant trade and politics.
Socrates was killed in 399 BC (see Trial of Socrates). In his speech (presented by Plato), he says the accusations were made by people who were jealous of him. He refused to defend himself.
He was the founder of political philosophy.
It was his habit to ask questions rather than to give conclusions. Many of his conversations end without a conclusion. He is known for this Socratic method.
Socrates taught that no one wants what is bad. So if anyone does something bad, it must be unintentional, out of ignorance. He concludes that all virtue is knowledge. He often talks about his own ignorance.
Plato's dialogues, and Aristotle, influenced the Roman empire, the Islamic Golden Age, and the Renaissance.
Plato
Plato was from Athens. He came a generation after Socrates. He wrote thirty-six dialogues and thirteen letters to Socrates, though some may be fake.
Plato's dialogues have Socrates. Along with Xenophon, Plato is the primary source of information about Socrates' life. Socrates was known for irony and not often giving own opinions.
Plato wrote the Republic, the Laws, and the Statesman. The Republic says there will not be justice in cities unless they are ruled by philosopher kings; those who enforcing the laws should treat their women, children, and property in common; and the individual should tell noble lies to promote the common good. The Republic says that such a city is likely impossible as it thinks philosophers would refuse to rule and the people would refuse to be ruled by philosophers.
Plato is known for his theory of forms. It says that there are non-physical abstract ideas that have the highest form and most real kind of reality.
Aristotle
Aristotle moved to Athens in 367 BC and began to study philosophy. He studied at Plato's Academy. He left Athens twenty years later to study botany and zoology. He became a teacher of Alexander the Great and returned to Athens ten years later to create his own school: the Lyceum. At least twenty-nine of his books have survived, known as the corpus Aristotelicum. He wrote about logic, physics, optics, metaphysics, ethics, rhetoric, politics, poetry, botany, and zoology.
Aristotle disagreed with his teacher Plato. He criticizes the governments in Plato's Republic and Laws, and refers to the theory of forms as "empty words and poetic metaphors." He cares more about empirical observation and practical concerns.
Aristotle was not that famous during the Hellenistic period, when Stoic logic was still popular. But later people popularized his work, which influenced Islamic, Jewish, and Christian philosophy. Avicenna referred to him simply as "the Master"; Maimonides, Alfarabi, Averroes, and Aquinas referred to him as "the Philosopher."
Hellenistic philosophy
During the hellenistic and Roman periods, many different schools of thought developed in the the Greco-Roman world. Greeks, Romans, Egyptians, Syrians and Arabs contributed. Persian philosophy and Indian philosophy also had an influence.
The spread of Christianity followed by the spread of Islam spread Hellenistic philosophy. It influenced the three Abrahamic traditions: Jewish philosophy, Christian philosophy, and early Islamic philosophy.
Islam
During the Middle Ages, Greek ideas were largely forgotten in Western Europe due to the migration period, which caused a decline in literacy. In the Byzantine Empire Greek ideas were kept and studied.
After the expansion of Islam, the Abbasid caliphs started translating Greek philosophy. Islamic philosophers such as Al-Kindi (Alkindus), Al-Farabi (Alpharabius), Ibn Sina (Avicenna) and Ibn Rushd (Averroes) reinterpreted these works. During the High Middle Ages Greek philosophy re-entered the West through translations from Arabic to Latin and also from the Byzantine Empire.
The re-introduction of these philosophies, plus new Arabic commentaries, had great influence on medieval philosophers such as Thomas Aquinas. Some Arab translators threw away books that disagreed with Islam. For example, Al-Mansur Ibn and Abi Aamir burned the Al-hakam II Library in Cordoba in 976.