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The book is an introduction to the science and possible applications of Graphene, the first one-atom-thick crystalline form of matter. Discovered in 2004 by now Nobelists Geim and Novoselov, the single layer of graphite, a hexagonal network of carbon atoms, has astonishing electrical and mechanical properties. It supports the highest electrical current density of any material, far exceeding metals copper and silver. Its absolute minimum thickness, 0.34 nanometers, provides an inherent advantage in possible forms of digital electronics past the era of Moore's Law. The book describes the unusual physics of the material, that it offers linear rather than parabolic energy bands. The Dirac-like electron energy bands lead to high constant carrier speed, similar to light photons. The lattice symmetry further implies a two-component wave-function, which has a practical effect of cancelling direct backscattering of carriers.