Poincaré theorem may refer to:
Poincaré conjecture, on homeomorphisms to the sphere; Poincaré recurrence theorem, on sufficient conditions for recurrence to take place in dynamical systems; Poincaré-Bendixson theorem, on the existence of attractors for two-dimensional dynamical systems; Poincaré–Birkhoff–Witt theorem, concerning Lie algebras and their universal envelopes; Poincaré lemma.