Abstract:   

   The Selberg Trace Formula gives a relation between the spectrum of a Riemann surface and its dynamics (closed geodesics). It is a noncommutative analogue of the Poisson Summation Formula. We will explain how a Riemann surface is obtained as a quotient of the upper half-plane, and how this gives a way to see the closed geodesics. Then we will formulate Selberg's Trace Formula, and as an application, derive Weyl's asymptotic law. .