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Compatibilism
Compatibilism is the philosophical position that determinism and free will are compatible. Free will, on this view, requires not the ability to have done otherwise in a strict causal sense, but the ability to act in accordance with one's own reasons and rational deliberation, unimpeded by external constraint.
Determinism
Determinism is the thesis that every event in the universe is necessitated by prior causes together with the laws of nature, so that given the complete state of the world at any moment, every subsequent state is uniquely determined.
Incompatibilism
Incompatibilism holds that free will and causal determinism cannot both be true, so that if every event is necessitated by prior causes then no one ever genuinely could have acted otherwise. The position encompasses both hard determinism, which accepts determinism and denies free will, and libertarian free will, which preserves agency by denying that the physical world is fully determined.
Libertarian free will
Libertarian free will (in the metaphysical sense, not the political sense) is the view that human beings possess a genuine capacity to choose between alternatives, that at least some actions are not determined by prior causes, and that this indeterminacy is essential for genuine moral responsibility.