Progress in Mathematics

This book introduces geometric spectral theory in the context of Riemann surfaces. A comprehensive account is given of dramatic recent developments in the context of infinite-area hyperbolic surfaces. The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, spectral theory, and ergodic theory. The book highlights these connections, at a level accessible to graduate students and researchers from a wide range of fields.