The decomposition of the space L2(G(Q)\G(A)), where G is a
reductive group defined over Q and A is the ring of adeles of Q, is
a deep problem at the intersection of number and group theory.
Langlands reduced this decomposition to that of the (smaller)
spaces of cuspidal automorphic forms for certain subgroups of G.
This book describes this proof in detail. The starting point is the
theory of automorphic forms, which can also serve as a first step
towards understanding the Arthur-Selberg trace formula. To make the
book reasonably self-contained, the authors also provide essential
background in subjects such as: automorphic forms; Eisenstein
series; Eisenstein pseudo-series, and their properties. It is thus
also an introduction, suitable for graduate students, to the theory
of automorphic forms, the first written using contemporary
terminology. It will be welcomed by number theorists,
representation theorists and all whose work involves the Langlands
program.
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