"A study of this book will help the reader to firmly put seismology in the larger context of mathematical physics and to understand its range of validity. I would not like to miss it from my bookshelf." Klaus Helbig Rijksuniversiteit Utrecht "Michael Slawinski has written several outstanding books on seismology. Like the others, Waves and Rays in Seismology organizes and explains things remarkably well. Too often science texts get bogged down in detail so that one loses clear sight of the overall field. This is never the case with Slawinski's works. They are not only remarkable teaching texts, but, as the subtitle, Answers to Unasked Questions indicates, they also help to shape the field in a forward-looking way, something only the finest books can do." James Robert Brown University of Toronto, Canada The author dedicates this book to readers who are concerned with finding out the status of concepts, statements and hypotheses, and with clarifying and rearranging them in a logical order. It is thus not intended to teach tools and techniques of the trade, but to discuss the foundations on which seismology - and in a larger sense, the theory of wave propagation in solids - is built. A key question is: why and to what degree can a theory developed for an elastic continuum be used to investigate the propagation of waves in the Earth, which is neither a continuum nor fully elastic. But the scrutiny of the foundations goes much deeper: material symmetry, effective tensors, equivalent media; the influence (or, rather, the lack thereof) of gravitational and thermal effects and the rotation of the Earth, are discussed ab initio. The variational principles of Fermat and Hamilton and their consequences for the propagation of elastic waves, causality, Noether's theorem and its consequences on conservation of energy and conservation of linear momentum are but a few topics that are investigated in the process to establish seismology as a science and to investigate its relation to subjects like realism and empiricism in natural sciences, to the nature of explanations and predictions, and to experimental verification and refutation.