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. The present 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 have also provided essential background to subjects such as
automorphic forms Eisenstein series Eisenstein pseudo-series (or wave-packets) and their
properties. It is thus also an introduction suitable for graduate students to the theory of
automorphic forms written using contemporary terminology. It will be welcomed by number
theorists representation theorists and all whose work involves the Langlands program.
