  The review is devoted to explanation of SERS in terms of the dipole and
quadrupole light-molecule interactions arising in surface fields strongly
varying in space in the region of the strongly irregular surface roughness. The
main SERS characteristics, the theory of electromagnetic fields near some model
kinds of rough surfaces and some other systems, the theory of SERS Raman tensor
for arbitrary and symmetrical molecules, selection rules and analysis of the
SER spectra, some anomalies in the SER spectra of symmetrical molecules for
some specific conditions, electrodynamic forbiddance of the quadrupole
scattering mechanism for the methane molecule and molecules with cubic symmetry
groups are considered. The huge enhancement and blinking of the SERS signal
arising in the phenomenon of Single Molecule detection by the SERS method are
explained. The above theory is compared with some another SERS mechanisms, and
the phenomena accompanying SERS are accounted for. It is demonstrated that the
theory is in a good agreement with the experiment and explains quite a number
of characteristics related to the SERS phenomenon.
