Leibniz argued that reality is ultimately composed of infinitely many simple, immaterial substances he called monads, each a self-contained perspective on the entire universe that develops according to its own internal principle without literally causally interacting with other monads; their apparent coordination is explained by a pre-established harmony instituted by God. In his "Theodicy" (1710) he argued this is the best of all possible worlds, the optimal arrangement compatible with the existence of genuine freedom and evil.
Intellectual setting
Leibniz worked as a diplomat and court official across the fragmented states of the Holy Roman Empire while independently developing the calculus at nearly the same time as Newton, a near-simultaneous discovery that produced a bitter priority dispute between their followers.
Key ideas
Monadology and pre-established harmony
Leibniz held that reality consists of infinitely many simple, "windowless" substances (monads), each unfolding its own internal states independently; their perfect coordination with one another is not causal interaction but a harmony pre-established by God at creation.
The best of all possible worlds
Leibniz argued that God, being perfectly good and rational, necessarily selected the most optimal among all logically possible worlds to create, so that the evil and imperfection this world contains are outweighed by its overall superiority to every alternative compossible arrangement.
Legacy
Leibniz's calculus notation remains in standard use today, his monadology influenced German idealism and twentieth-century process philosophy through Whitehead, and his "best of all possible worlds" doctrine became the target of Voltaire's satire in "Candide."