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This book is the fifteenth in a series of Proceedings for the Séminaire Poincaré, which is directed towards a broad audience of physicists, mathematicians, and philosophers of science.§§This new volume of the Poincaré Seminar Series, entitled Dirac Matter, corresponds to the eighteenth such seminar, held on June 28, 2014. Its aim is to provide a general introduction to the physics of materials, the conduction properties of which are due to electrons described by the Dirac equation. The latter was introduced by Paul Dirac in 1928 to describe a fast moving electron beyond the non-relativistic Schrödinger equation. It was recently realized that it gives the correct low-energy description of many condensed matter systems, such as graphene and topological insulators. The present volume explains why Dirac still matters. This book, by the breadth of topics covered in Dirac's unforeseen legacy in condensed matter physics, will be of broad interest to physicists, mathematicians, and historians of science.§§
