  Raman spectroscopy of graphene is reviewed from a theoretical perspective.
After an introduction of the building blocks (electronic band structure, phonon
dispersion, electron-phonon interaction, electron-light coupling), Raman
intensities are calculated using time-dependent perturbation theory. The
analysis of the contributing terms allows for an intuitive understanding of the
Raman peak positions and intensities. The Raman spectrum of pure graphene only
displays two principle peaks. Yet, their variation as a function of internal
and external parameters and the occurrence of secondary, defect-related peaks,
conveys a lot of information about the system. Thus, Raman spectroscopy is used
routinely to analyze layer number, defects, doping and strain of graphene
samples. At the same time, it is an intriguing playground to study the optical
properties of graphene.
