Graphene, a single sheet of graphite, has an unconventional electronic structure that can be described in terms of massless Dirac Fermions. This interesting electronic feature is not only an important fundamental issue in condensed matter physics but also holds future promise in post-Si electronic/spintronics device applications. Graphene is the most fundamental building block, with which a variety of carbon-based materials such as graphite, fullerene and carbon nanotubes can be created. The diverse chemical, electronic and magnetic properties of nanographene and graphene are mainly due to their geometrical electronic structure. This book presents the frontiers of graphene research ranging from important issues in condensed matter physics and chemistry to advanced device applications.