In this paper the theorem of Rado-Kneser-Choquet is extended in two different ways to multiply connected domains. One is a direct continuation of Kneser's idea and has nothing to do with convexity; while the other asserts that a finitely connected domain can be mapped harmonically with prescribed outer boundary correspondence onto a given convex domain with suitable punctures. It is also shown that a domain containing infinity admits a unique harmonic mapping, with standard normalization at infinity, onto a punctured plane. For domains of connectivity n the dilatation of the canonical mapping covers the unit disk exactly 2n times. Furthermore, no other normalized harmonic mapping has the same dilatation.