Development of the solid-state theory, essentially, the theory of imperfect metallic crystals and methods of investigation. Development of the kinematic and dynamical theories of diffraction and scattering, the theory of photons in crystals with defects, the theory of phase transformations, structural changes, and diffusion in interstitial, substitutional, and subtraction alloys. Development of theoretical and experimental grounds of new techniquesfor diagnosticsof crystalline and non-crystalline (medical-biological) objects on the basis of multiple wave scattering effects, particularly, on the beams of synchrotron radiation and neutrons. Researches of the crystallographic, statistical-thermodynamic, and synergetic aspects of the order–disorder and order–order phase transformations as well as the interplay of atomic and magnetic orders, physical kinetics of short-range and long-range orderings of solid solutions under action of external fields and radiations. Finding-out of self-organized mechanisms of atomic, electronic, and magnetic orderings of low-dimensional structures with controlled functional, in particular, transport, properties.