  This article reviews the basic theoretical aspects of graphene, a one atom
thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic
excitations. The Dirac electrons can be controlled by application of external
electric and magnetic fields, or by altering sample geometry and/or topology.
We show that the Dirac electrons behave in unusual ways in tunneling,
confinement, and integer quantum Hall effect. We discuss the electronic
properties of graphene stacks and show that they vary with stacking order and
number of layers. Edge (surface) states in graphene are strongly dependent on
the edge termination (zigzag or armchair) and affect the physical properties of
nanoribbons. We also discuss how different types of disorder modify the Dirac
equation leading to unusual spectroscopic and transport properties. The effects
of electron-electron and electron-phonon interactions in single layer and
multilayer graphene are also presented.
