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Allegory of the Cave
The Allegory of the Cave is Plato's famous image in Book VII of the Republic, depicting prisoners chained in a cave who mistake shadows for reality, illustrating the ascent of the soul from ignorance to knowledge of the Forms.
Legitimacy
Legitimacy in political philosophy refers to the moral right of a government to exercise authority and the corresponding obligation of citizens to obey its laws. Theories of legitimacy range from consent-based accounts, which ground authority in the agreement of the governed, to procedural accounts that locate it in fair institutional processes, and substantive accounts that tie it to the government's delivery of justice and the common good.
Philosopher-king
In Plato's Republic, the philosopher-king is a ruler who possesses genuine knowledge of the Forms and governs the ideal state on the basis of wisdom rather than popular opinion or personal ambition.