The main research work of the Department deals with the system and symmetry analysis of multi-level objects of nature, socially organized and ideal systems. The scientific supervisor is Prof. E. Khakimov. Based on the theoretical and methodological principles of the theory of hierarchy, Prof. E. Khakimov together with his colleagues have developed a model of structural organization which represents a system of dual nature the description of which is associated with a change of scale and symmetry within the transition of the system from one level of organization to a more complex one. Professors N. Karogodin (Institute of Geology and Geophysics of SB RAS, ISU), E. Soroko (National Academy of Belarus), A. Uemov and L. Terentyeva (Odessa National University named after I. Mechnikov, Ukraine), N. Nizamutdinov (Volga Region Federal University - KSU) and others carry our joint research in the area. A number of works have been published jointly with Prof. A. Trofimov, Y. Karogodin, N. Nizamutdinov, etc.