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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, in words of Mario Bunge. 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 questions is: why and to what extent 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 (lack thereof) of gravitational and thermal effects and the rotation of the Earth, are discussed ab initio.