After Socrates' death, Plato, among others, withdrew from the city of Athens. He took up residence in the city of Megara.
Plato visited Italy twice. Once was to meet the Pythagoras philosophers and the other to influence Sicily's government. He was unsuccessful in the latter.
Some Prisoners would mistake appearance for reality. They would think the things they see on the wall (the shadows) were real instead of what really causes the shadows.
In the allegory of the Cave, Plato likens people untutored in the Theory of Forms to prisoners chained in a cave, unable to turn their heads. All they can see is the wall of the cave. Puppeteers, who are behind the prisoners, hold up puppets that cast shadows on the wall of the cave.
After his death, Plato's nephew succeeded him at the head of the Academy. Aristotle, being as he had been a student and teacher at the Academy for over twenty years, felt he should have succeeded Plato.
Plato was a teacher and administrator of the "Academy", which quickly attracted a great number of outstanding students and faculty. Aristotle, studied and taught at the Academy before he founded his own school.
Plato engaged in many forms of poetry as a young man, only later turning to philosophy. Upon meeting Socrates, however, Plato directed his inquiries toward the question of virtue.
Most scholars agree that shortly after 399 Plato began to write extensively. It is not known if Plato began to write philosophically before or after Socrates' execution.
Plato grew up during the Peloponnesian War. It is likely, but unconfirmed, that he served in the cavalry in campaigns against Sparta.
Plato was very devoted to Socrates. Based on his background, he should have entered a political career, but Socrates' trial and death made Plato disillusioned with politics.