This is a thoroughly revised version of the original book published in 1986. About half of the contents of the previous version remain essentially unchanged, and one quarter has been rewritten and updated. The rest consists of completely new and extended material. Recent research has focussed on new materials made through "molecular engineering", and computational materials science through ab initio electron structure calculations. Another trend is the ever growing interdisciplinary aspect of both basic and applied materials science. There is an obvious need for reviews that link well established results to the modern approaches. One purpose of this book is to provide such an overview in a specific field of materials science, namely thermophysical phenomena that are intimately connected with the lattice vibrations of solids. This includes, e.g., elastic properties and electrical and thermal transport. Furthermore, this book attempts to present the results in such a form that the reader can clearly see their domain of applicability, for instance if and how they depend on crystal structure, defects, applied pressure, crystal anisotropy etc. The level and presentation is such that the results can be immediately used in research. Graduate students in condensed matter physics, metallurgy, inorganic chemistry or geophysical materials will benefit from this book as will theoretical physicists and scientists in industrial research laboratories.