This advanced and notable method was developed to overcome some ambiguities in terminating the hierarchy of the equations of motion of double-time Green functions and to give a workable technique to systematic way of decoupling.

The approach provides a practical method for description of the many-body quasi-particle dynamics of correlated systems on a lattice with complex spectra.

Moreover, this method provides a very compact and self-consistent way of taking into account the damping effects and finite lifetimes of quasi-particles due to inelastic collisions.

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.

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.

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 chief purposes of that study were to demonstrate the connection and interrelation of these conceptual advances of the many-body physics and to try to show explicitly that those concepts, though different in details, have a certain common features.

Several problems in the field of statistical physics of complex materials and systems (e.g. the chirality of molecules) and the foundations of the microscopic theory of magnetism and superconductivity were discussed in relation to these ideas.

The results of investigation of the dynamic behavior of a particle in an environment, taking into account dissipative effects, were considered and applied to a variety of concrete problems.