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This book develops the subject from the basic principles of quantum mechanics. The emphasis is on a single statement of the ideas underlying the various approximations that have to be used and care is taken to separate sound arguments from conjecture. This book is written for the student of theoretical physics who wants to work in the field of solids and for the experimenter with a knowledge of quantum theory who is not content to take other people's arguments for granted. The treatment covers the electron theory of metals as well as the dynamics of crystals, including the author's work on the thermal conductivity of crystals which has been previously published in English.