In the present monograph the evolution of a two-level system in the external resonant field is investigated beyond the framework of commonly used approximations. Rapidly converging algorithm for the numerical solution and analytical approximation that is valid within the whole range of the parameter variation are deduced. A set of new quantum and non-perturbative effects in the behavior of the system beyond the rotating-wave approximation, Markovian approximation and classical field approximation is described. The obtained solutions can be used for theoretical explanation of some experimental data in the limit of strong coupling and high excitations (intensities) of the external fields. These solutions can be used as the initial approximation for more accurate description of relaxation processes that take place in real systems as well.