One Teacher, Several Heirs
Socrates left no doctrine, so his followers took quite different things from him, and the disagreement is evidence about how open his practice really was.
The Cynics, from Antisthenes and Diogenes, took the priority of virtue to its conclusion: if virtue is sufficient for happiness, everything else — property, reputation, comfort, convention — is worthless. Diogenes lived in a jar, discarded his cup on seeing a child drink from cupped hands, and told Alexander the Great to stop blocking his sunlight. The point of the theatre was to show that convention has no authority.
The Cyrenaics, from Aristippus, drew the opposite conclusion: the good is immediate pleasure, since only present sensation is certainly known. Where the Cynics minimised needs, the Cyrenaics maximised enjoyment, yet both claimed the same teacher.
The Megarians, from Euclides, combined Socratic ethics with Eleatic logic and produced the paradoxes: the Liar ("this sentence is false") and the Sorites (one grain is not a heap; adding one grain never makes a heap; so no number of grains is a heap). These are still live problems.
Plato is the heir who transformed the inheritance. His theory of Forms answers a question the elenchus kept raising: Socrates asks what justice is, and the answers keep failing because they give examples rather than the thing itself. Plato's response is that the thing itself exists, a perfect, unchanging, non-spatial Form of justice, which particular just acts imperfectly resemble.
The theory also settles Heraclitus against Parmenides by giving each a domain: the sensible world genuinely flows, and the world of Forms genuinely does not. Both were right about different things.
The divided line in the Republic sets out four levels of cognition — imagination, belief, reasoning, understanding — and contains a nice mathematical fact. Divide a line unequally, then divide each part in the same ratio, and the two middle segments come out exactly equal, whichever ratio you chose. Plato uses that equality to mark belief and reasoning as the two intermediate states.
Common pitfall: treating the Forms as an obvious mystification. They answer a real problem: definitions by example fail, yet we manage to apply "just" to new cases, so something must be shared. Whether that something is a separate entity is exactly what Aristotle would go on to dispute.