Liquid crystals were discovered at the end of the 19th century. With properties intermediate between those of solids and liquids, they are known primarily for their widespread use in displays. However, even more important is the fact that they allow us to perform (sometimes very simple) experiments which provide insight into fundamental problems of modern physics, such as phase transitions, frustration, hydrodynamics, defects, nonlinear optics, or surface instabilities. It is in this spirit that we conceived this book, without attempting to exhaustively describe the physical properties of liquid crystals. From this point of view, the book is far from complete; it only reflects a very small part of the enormous work done on this subject over the last thirty years. On the other hand, it provides a thorough treatment of topics reflecting the research interests of the authors, such as growth phenomena, flow and thermal instabilities, or anchoring transitions, which are not described in detail in the fundamental (and already well-known) treatises by P.-G. de Gennes and J. Prost [1], S. Chandrasekhar [2], or P. J. Collings and M. Hird [3]. We also recommend M.Kléman’s book on the physics of defects [4] as well as P.M. Chaikin and T.C. Lubensky’s book [5], which discusses the general principles of condensed matter physics, often using liquid crystals as an illustration.