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The description of the symmetry operations of crystals and of the resulting physical properties is the aim of the present book. This clear and rigorous book is divided in three parts: 1) a first part on crystal symmetry, symmetry operations, crystal lattices, point groups and space groups; 2) a second part on crystal anisotropy and tensors applied to elasticity, propagation of elastic waves in crystals and piezoelectricity; 3) a third one on the optical properties of crystals, polarization, optical activity and electro-optical effects. The various types of chemical bonds are also described in a small chapter between the first and the second parts. Most chapters include an annex on a particular topic related to one of the points developed in the chapter, aimed at exciting the curiosity of the reader and these complements are a real added value to the book. Exercises are also included, the solutions of which are provided as supplementary online materials. The book will be essential reading for graduate student in solid state chemistry, condensed matter physics, mineralogy and materials science.