2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76182The goal of the course was a review of results mainly due to M. Olbrich and the first author. We consider a discrete cocompact subgroup $Γ$ of a semisimple Lie group $G$. We relate the group cohomology of $Γ$ with coefficients in the maximal globalization of a representation of $G$ with the multiplicities of unitary representations of $G$ in $L^2(G/Γ)$. Explicit calculations are given in the case $G=SL(2,R)$. In the rank-one case we state a version of the Selberg trace formula, discuss the singularities of the Selberg zeta-functions, and state their relation with the cohomology of $Γ$ in principal series representations.11 pages, Notes of a course given at the Summer School "Algebraic Groups" in Goettingen, June 27 - July 15Representation TheoryDifferential Geometrytext