Volume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

Paul Garrett is Professor of Mathematics at the University of Minnesota. His research focuses on analytical issues in the theory of automorphic forms. He has published numerous journal articles as well as five books.

1. Four small examples; 2. The quotient Z+GL2(k)/GL2(A); 3. SL3(Z), SL5(Z); 4. Invariant differential operators; 5. Integration on quotients; 6. Action of G on function spaces on G; 7. Discrete decomposition of cuspforms; 8. Moderate growth functions, theory of the constant term; 9. Unbounded operators on Hilbert spaces; 10. Discrete decomposition of pseudo-cuspforms; 11. Meromorphic continuation of Eisenstein series; 12. Global automorphic Sobolev spaces, Green's functions; 13. Examples ¿ topologies on natural function spaces; 14. Vector-valued integrals; 15. Differentiable vector-valued functions; 16. Asymptotic expansions.