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.
The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall
effect. The electronic properties of graphene stacks are discussed and vary with stacking order and
number of layers. Edgesurface states in graphene depend on the edge termination zigzag or
armchair and affect the physical properties of nanoribbons. 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.