Automorphic Forms on Sl2 (R)This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper half plane X, with respect to a discrete subgroup D*G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of