Hyperbolic geometry is a classical subject in pure mathematics
which has exciting applications in theoretical physics. In this
book leading experts introduce hyperbolic geometry and Maass
waveforms and discuss applications in quantum chaos and cosmology.
The book begins with an introductory chapter detailing the geometry
of hyperbolic surfaces and includes numerous worked examples and
exercises to give the reader a solid foundation for the rest of the
book. In later chapters the classical version of Selberg's trace
formula is derived in detail and transfer operators are developed
as tools in the spectral theory of Laplace-Beltrami operators on
modular surfaces. The computation of Maass waveforms and associated
eigenvalues of the hyperbolic Laplacian on hyperbolic manifolds are
also presented in a comprehensive way. This book will be valuable
to graduate students and young researchers, as well as for those
experienced scientists who want a detailed exposition of the
subject.
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