damping effects and finite lifetimes of quasi-particles due to inelastic collisions. In addition, it correctly defines the Generalized Mean Field (GMF), that determine elastic scattering renormalizations and, in general, are not functionals of the mean particle densities only. Applications to the lattice fermion models such as Hubbard/Anderson models and to the Heisenberg model of ferro- and antiferromagnet, which manifest the operational ability of the method were given. It was shown that the IGF method provides a powerful tool for the construction of essentially new dynamical solutions for strongly interacting many-particle systems with complex spectra. Kuzemsky derived a new self-consistent solution of the Hubbard model in the (1973–1978, a notable contribution to the theory of strongly correlated electron systems. He also published a notable work on the quantum protectorate. Some physical implications involved in a new concept, termed the "quantum protectorate" (QP), invented by R. Laughlin and D. Pines were developed and discussed. This was done by considering the idea of quantum protectorate in the context of quantum theory of magnetism. It was suggested that the difficulties in the formulation of quantum theory of magnetism at the microscopic level, that are related to the choice of relevant models, can be understood better in the light of the QP concept. It was argued that the difficulties in the formulation of adequate microscopic models of electron and magnetic properties of materials are intimately related to dual, itinerant and localized behaviour of electrons. A criterion of what basic picture describes best this dual behaviour was formulated. The main suggestion was that quasi-particle excitation spectra might provide distinctive signatures and good criteria for the appropriate choice of the relevant model. The concepts of broken symmetry, quantum protectorate, and Bogoliubov's quasi-averages were analyzed in the context of quantum theory of magnetism and theory of superconductivity. In this interdisciplinary study he focused on the applications of the symmetry principles to quantum and statistical physics in connection with some other branches of science. The profound and innovative idea of quasiaverages formulated by N. N. Bogoliubov, gives the so-called macro-objectivation of the degeneracy in domain of quantum statistical mechanics, quantum field theory and in the quantum physics in general. He discussed there the complementary unifying ideas of modern physics, namely: spontaneous symmetry breaking, quantum protectorate and emergence. The interrelation of the concepts of symmetry breaking, quasiaverages and quantum protectorate was analyzed in the context of quantum theory and statistical