In mathematics, there are two basic results in Lie group theory that go by the name Cartan's theorem. They are both named for Élie Cartan.

1. The theorem that for a Lie group G, any closed subgroup is a Lie subgroup.

2. A theorem on highest weight vectors in the representation theory of a semisimple Lie group.

See also Cartan's theorems A and B, results of Henri Cartan.