Plato (428/427 BC - 348/347 BC), was a Classical Greek philosopher, who, together with his mentor, Socrates, and his student, Aristotle, helped to lay the foundations of Western philosophy. Plato was also a mathematician, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the western world. Plato was originally a student of Socrates, and was as much influenced by his thinking as by what he saw as his teacher's unjust death.
Plato's sophistication as a writer can be witnessed by reading his Socratic dialogues. Some of the dialogues, letters, and other works that are ascribed to him are considered spurious. Although there is little question that Plato lectured at the Academy that he founded, the pedagogical function of his dialogues, if any, is not known with certainty. The dialogues have since Plato's time been used to teach a range of subjects, mostly including philosophy, logic, rhetoric, mathematics, and other subjects about which he wrote.
According to Diogenes Laertius, the philosopher was named Aristocles after his grandfather, but his wrestling coach, Ariston of Argos, dubbed him "Platon", meaning "broad," on account of his robust figure. According to the sources mentioned by Diogenes, Plato derived his name from the breadth (platytes) of his eloquence, or else because he was very wide (platys) across the forehead. In the 21st century some scholars disputed Diogenes, and argued that the legend about his name being Aristocles originated in the Hellenistic age.
Speusippus praised Plato's quickness of mind and modesty as a boy, and the "first fruits of his youth infused with hard work and love of study". Plato must have been instructed in grammar, music, and gymnastics by the most distinguished teachers of his time. Plato had also attended courses of philosophy before meeting Socrates.
Plato may have traveled in Italy, Sicily, Egypt and Cyrene. Said to have returned to Athens at the age of forty, Plato founded one of the earliest known organized schools in Western Civilization on a plot of land in the Grove of Hecademus or Academus. The Academy was "a large enclosure of ground which was once the property of a citizen at Athens named Academus... some, however, say that it received its name from an ancient hero", and it operated until AD 529, when it was closed by Justinian I of Byzantium, who saw it as a threat to the propagation of Christianity. Many intellectuals were schooled in the Academy, the most prominent one being Aristotle.
Much on Plato's mind is the father-son relationship, the "question" of whether a father's interest in his sons has much to do with how well his sons turn out. A boy in ancient Athens was socially located by his family identity, and Plato often refers to his characters in terms of their paternal and fraternal relationships. Socrates was not a family man, and saw himself as the son of his mother, who was apparently a midwife. A divine fatalist, Socrates mocks men who spent exorbitant fees on tutors and trainers for their sons, and repeatedly ventures the idea that good character is a gift from the gods.
"Platonism" is a term coined by scholars to refer to the intellectual consequences of denying, as Socrates often does, the reality of the material world. In several dialogues, most notably the Republic, Socrates inverts the common man's intuition about what is knowable and what is real. While most people take the objects of their senses to be real if anything is, Socrates is contemptuous of people who think that something has to be graspable in the hands to be real.
The allegory of the cave (often said by scholars to represent Plato's own epistemology and metaphysics) is intimately connected to his political ideology (often said to also be Plato's own), that only people who have climbed out of the cave and cast their eyes on a vision of goodness are fit to rule. The "Theory of Forms" typically refers to Plato's belief that the material world as it seems to us is not the real world, but only a shadow of the real world. Plato spoke of forms in formulating his solution to the problem of universals. The forms, according to Plato, are roughly speaking archetypes or abstract representations of the many types and properties (that is, of universals) of things we see all around us.
Much more to read at Wikipedia: Plato