  A review of electronic dynamics of single-impurity and many-impurity Anderson
models is contained in this report. Those models are used widely for many of
the applications in diverse fields of interest, such as surface physics, theory
of chemisorption and adsorbate reactions on metal surfaces, physics of
intermediate valence systems, theory of heavy fermions, physics of quantum dots
and other nanostructures. While standard treatments are generally based on
perturbation methods, our approach is based on the non-perturbative technique
for the thermodynamic Green functions. The method of the irreducible Green
functions is used as the basic tool. This irreducible Green functions method
allows one to describe the quasiparticle spectra with damping of the strongly
correlated electron systems in a very general and natural way and to construct
the relevant dynamical solution in a self-consistent way on the level of Dyson
equation without decoupling the chain of the equations of motion for the Green
functions. The subject matter includes the improved interpolating solution of
the Anderson model. It was shown that an interpolating approximation, which
simultaneously reproduces the weak-coupling limit up to second order in the
interaction strength U and the strong-coupling limit up to second order in the
hybridization V (and thus also fulfils the atomic limit) can be formulated
self-consistently. This approach offers a new way for the systematic
construction of approximate interpolation dynamical solutions of strongly
correlated electron systems.
