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The use of single crystals for scientific and technological applications is now widespread in solid-state phyiscs, optics, electronics, materials science and geophysics. An understanding of the variation of physical properties with crystalline direction is essential to maximize the performance of solid-state devices. This is the second edition of an established textbook. The book provides a concise introduction to the tensor properties of crystals at a level suitable for advanced undergraduate and graduate students. It is written from a physical viewpoint and avoids advanced mathematics. For this second edition, the successful basic format of the book has been retained with corrections and updating where needed. With the increasing importance of non-linear optics a new chapter on optoelectronics has been added. A short discussion of incommensurate modulated structures has been included in the final chapter because they are relevant to high temperature superconductors and to ferroelectric and ferromagnetic materials. Extensive use of diagrams, worked examples and problems with answers is made throughout.