•Why it earns a slot
The book that reframed political legitimacy as something built from the consent and collective will of the governed rather than inherited authority, directly cited by the architects of the French Revolution.
Rousseau opens with one of philosophy's most quoted lines and spends the rest of the book explaining what could possibly make political authority legitimate. His answer is the social contract: individuals surrender themselves entirely to the community as a whole, not to a king or master, and in exchange gain a share in the 'general will' that governs everyone equally.
This distillation is written from the freely available original, which is always the better read when you have the time: Project Gutenberg.