This book is devoted to explanation of SERS in terms of the strong dipole and especially quadruple light-molecule interactions arising in surface fields strongly varying in space in the region of strongly irregular surface roughness. The influence of the quadruple interaction is a matter of principle, since it provides explanation for the appearance of forbidden bands arising in a great number of experiments on SERS on symmetrical molecules. This essential detail in fact is absent in all other SERS theories, that does not permit to create a closed theory, which explains the majority of experimental facts accompanying SERS by a unitary approach. Moreover as it is demonstrated in the book the huge enhancement in the phenomenon of Single Molecule Detection by the SERS method can be explained exclusively by the strong quadruple light-molecule interaction. The first part of the book is devoted to a brief description of main SERS characteristics and critical analysis of theoretical approaches. Further the theory of electromagnetic field near some model kinds of rough surfaces and some other systems and the theory of the SER cross-section for arbitrary and symmetrical molecules are presented in detail. The obtained expressions helps to establish selection rules for contributions in the SER cross-section and analyse the SER spectra of symmetrical molecules. This analysis corroborates main specific features of the SER spectra of symmetrical molecules and some anomalies, which exist in these spectra for some specific conditions. The existence of electrodynamic forbiddance of the quadruple scattering mechanism for the methane molecule and molecules with cubic symmetry groups is established. The above theory permits to explain not only the huge enhancement in the phenomenon of Single -Molecule Detection but the blinking of the SERS signal too. The first layer effect, arising in the first layer of absorbed molecules also is considered in detail. It appears that the nature of this phenomenon is the electrodynamic enhancement, which is very large just in the first layer. The other phenomena, accompanying SERS are accounted for. It is demonstrated that the theory is in a good agreement with the SERS experiments and explains quite a number of characteristics related to the SERS phenomenon.