The theory of automorphic forms, which goes back to the work of Poincare and Klein, has been considerably developed and generalized in the last 40 years by the use of new analytic methods, inspired in part by harmonic analysis on Lie groups. This book is devoted to the analytic theory of automorphic forms, limited to the case of fuchsian groups, but from those more general points of view.This first exposition of this approach in this special case should be accessible to researchers and graduate students having some familiarity with functional analysis and elementary Lie theory.

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