Graphene : carbon in two dimensions Graphene is the thinnest known material a sheet of carbon atoms arranged in hexagonal cells a single atom thick and yet stronger than diamond. It has potentially significant applications in nanotechnology beyond silicon electronics solid state realization of high energy phenomena and as a prototype membrane which could revolutionise soft matter and 2D physics. In this book leading graphene research theorist Mikhail Katsnelson presents the basic concepts of graphene physics. Topics covered include Berry phase topologically protected zero modes Klein tunneling vacuum reconstruction near supercritical charges and deformation induced gauge fields. The book also introduces the theory of flexible membranes relevant to graphene physics and discusses electronic transport optical properties magnetism and spintronics. Standard undergraduate level knowledge of quantum and statistical physics and solid state theory is assumed. This is an important textbook for graduate students in nanoscience and nanotechnology and an excellent introduction for physicists and materials science researchers working in related areas