The Cauchy-Davenport theorem is the starting point for a large branch of combinatorial number theory. This theorem gives a natural lower bound on the size of the sumset $A+B$ whenever $A$ and $B$ are subsets of the group of integers modulo a prime p. More precisely, they prove that $|A+B| \ge \min\{p,|A|+|B|-1\}$. M. Kneser obtained a generalization of the Cauchy-Davenport theorem to all abelian groups. He proved that for every pair of finite sets $A,B$ there is a subgroup $H$ so that $A+H+B = A+B$ and $|A+B| \ge |A| + |B| - |H|$. Here we generalize these results to arbitrary groups (which we now write multiplicatively). We show that for every pair $A,B$ there exists a subgroup $H$ so that $|AB| \ge |A| + |B| - |H|$ and so that for every $a \in A$ there exists a subgroup $K$ conjugate to $H$ with $aKB \subseteq AB$.