Table of Contents

Preliminary remarks on topological groups.- Automorphism groups of bilinear forms.- Geometry in the representation space.- Symplectic geometry.- Weakly symmetric Riemannian spaces.- The Riemannian space of all positive matrices.- A generalization of JS(X).- The Riemannian space .- The reduction theory of positive quadratic forms.- Größen-characters of quadratic forms.- The modular group of degree n.- The fundamental domain of the modular group.- Modular forms of degree n.- Report on Eisenstein series of the modular group.- Dirichlet series corresponding to modular forms.- Zeta functions attached to quadratic forms.- Selberg's zeta functions.- Non-analytic Eisenstein series.- The differential operaton M?.- Final aspects.