This book consists of two parts. The first part gives a general introduction to the modern theory of automorphic forms with applications to spectral questions. In particular, it deals with the spectrum of differential forms on congruence hyperbolic manifolds. It contains, for example, the Selberg type theorem on the first eigenvalue of the Laplace operator acting on differential forms, using representation theoretic methods and techniques of proof. The second part of the book has a more differential geometric flavour. The main motivation of this chapter comes from Arthur conjectures, which imply strong restrictions on the spectrum of arithmetic manifolds and conjectural properties of the geometry of hyperbolic manifolds (proved in a weak form in some particular cases).