Abstract: The cohomology of an aspherical space equals the cohomology of the corresponding fundamental group. For congruence groups such as GL(n, Z), we determine its low degree cohomologies (with complex coefficients). Our method is analytic and representation theoretic. Basic theory of continuous cohomologies, and Franke's filtration of the space of automorphic forms will be reviewed. This is a joint work with Jian-Shu Li.