From the reviews: "The book under review ... provides an introduction to the general theory of semisimple or reductive groups G, with symmetric space G/K (K maximal compact). ... It is ... meant for experienced insiders, even as the presentation of the material is excellent and accessible. A well-prepared graduate student would do well with this book. More experienced analytic number theorists will find it enjoyable and spellbinding. ... I heartily recommend to other analytic number theorists of a similar disposition." (Michael Berg, MAA Online, December, 2008) "This book is part of a program of the authors to develop a systematic theory of theta and zeta functions on homogeneous spaces, using techniques of harmonic analysis and, in particular, heat kernels. ... the book includes many details that would likely have been left for the reader to work out by her/himself in a more streamlined monograph. ... all in all, an enjoyable book to read." (Fredrik Stromberg, Zentralblatt MATH, Vol. 1192, 2010)

• Gaussians, Spherical Inversion, and the Heat Kernel.- Spherical Inversion on SL2(C).- The Heat Gaussian and Heat Kernel.- QED, LEG, Transpose, and Casimir.- Enter ?: The General Trace Formula.- Convergence and Divergence of the Selberg Trace.- The Cuspidal and Noncuspidal Traces.- The Heat Kernel on ?\G/K.- The Fundamental Domain.- ?-Periodization of the Heat Kernel.- Heat Kernel Convolution on (?\G/K).- Fourier-Eisenstein Eigenfunction Expansions.- The Tube Domain for ??.- The ?/U-Fourier Expansion of Eisenstein Series.- Adjointness Formula and the ?\G-Eigenfunction Expansion.- The Eisenstein-Cuspidal Affair.- The Eisenstein Y-Asymptotics.- The Cuspidal Trace Y-Asymptotics.- Analytic Evaluations.