This book is made of two parts. The first is concerned with the differential
form spectrum of congruence hyperbolic manifolds. We prove Selberg type
theorems on the first eigenvalue of the laplacian on differential forms. The
method of proof is representation theoritic, we hope the different chapters may
as well serve as an introduction to the modern theory of automorphic forms and
its application to spectral questions. The second part of the book is of a more
differential geometric flavor, a new kind of lifting of cohomology classes is
proved.Comment: 237 pages, book (in french
