Abstract. It is well-known that the classical geodesic flow on the modular surface can be coded with the help of simple (Gauss) continued fractions and that the reduction theory of binary quadratic forms can be used to establish a connection between the transfer operator of the geodesic flow and the Selberg zeta function of the surface. In this setting it is also possible to relate eigenfunctions of the transfer operator directly to Maass waveforms via functional equations and cohomology (Lewis-Zagier theory of period functions). I will talk about work by Tobias Mühlenbruch, Dieter Mayer and myself aimed at generalizing these kinds of results from the Modular group to Hecke triangle groups.