[en] Full text: 1. The diffraction theory of elastic and inelastic scattering of hadron-hadron and hadron-nucleus processes is developed. The description of experimental data on differential cross section of elastic scattering p p, p-bar p in wide range of transferred momentum is made in the frames of the developed inelastic overlap function model. The investigation of nuclei elastic scattering at the low, middle and high energies is carried out, that allowed to execute quantitative control of efficiency or quantum-field and phenomenological theories and make critical analysis of their utility. The principle of construction of realistic amplitudes of the elastic scattering is confirmed on the basic of the s- and t-channel approaches both conditions stationary of amplitudes. For a wide range of models the comparative analysis of amplitude of inelastic scattering in representation of impact parameter is executed. The expression for effective radius of interaction, effective trajectory Regge and slope of inelastic function of overlapping are analysed. In diffraction approximation the satisfactory description of the data on hadrons interaction at the energy of tens GeV with proton and deuterons is received. The features of spectra of fast particles are analysed. The theory of collective variables S, T, P which characterize a deviation degree of angular distribution of particles from spherical symmetry, the general formula for dispersion of any density of obtained, the particles decays are investigated [1-2]. 2. The solution of Lippmann-Schwinger equation investigated within the frameworks of frameworks of high -energy approximation satisfies the generalized Huygens principle used in the diffraction theory nuclear processes. The diffraction emission is considered at the interaction of charged hadrons one with another and the nuclei [3]. 3. Study of elastic interactions of hadrons at high energies is of great interest due to the fact that the amplitude of this process is the simplest, and at the same time, it is a fundamental object for theoretical and experimental researches. Study of this process allows one to have a quantitative check of various theories and experimental researches. Study of this process allows one to have a quantitative check of various theories and models, and to make a critical selection. By using of fundamental property of theory-unitarity condition of scattering matrix- elastic scattering can be connected with inelastic reaction. Based on S-channel unitarity condition expressing elastic amplitude via inelastic overlapping function, it is important to study the latter, as well as to describe the experimentally measured characteristics of hadron-nucleon interaction at high-energies and to have results prediction. By using experimental data on differential cross section elastic scattering of hadrons at various energies and by theoretical information on ratio of a real part and an imaginary part of scattering amplitude δ(t) the t- dependence of inelastic and elastic overlapping functions is studied. Influence of a zigzag from differential cross-section of elastic p p( p-bar) scattering on profile function and inelastic overlapping function to violation of geometric scaling was studied. In frames of scaling the general expressions for s- and t- dependences of inelastic and elastic overlapping function are derived. Comparison of this function in three elastic scattering models was carried out. It was demonstrated that one would need to assume that hadrons become blacker at central part in order to correctly describe experimental angular distribution data. Dependence of differential cross-section on transfer momentum square for elastic hadron scattering at energies of ISR and SPS in the model of inelastic overlapping function is studied [1-2]. (author)