The project explores the electronic structure of strongly correlated transition metal compounds in which, due to strong intra-atomic Coulomb interactions, an energy gap or pseudogap is formed in the spectrum of strongly correlated d- and f-electrons. Such systems include strongly correlated insulators, helicoidal ferromagnets with skyrmion phases. These systems have promising electronic and spin properties insufficiently studied so far that are important for applications in microelectronics. The state diagrams including skyrmion phases arising in a magnetic field in chiral magnets, phases with non-phonon superconductivity (occurring in the crossover region of magnetic ordering and superconductivity) have not yet been studied. The difficulties in solving these problems are due to the proximity of the empirical diagrams of the ground state of this systems to the metal-insulator electronic transition, as well as the features of not only thermodynamic, but also quantum criticality, observed during temperature phase transitions. Within the framework of the project, we will construct and analyze equations of magnetic states based on LDA + U + SO calculations of the electronic structure, a model description of strongly correlated d, f- electronic systems with intra-atomic Coulomb and spin-orbit interactions, and the Dzyaloshinsky-Moria relativistic exchange. It is planned to study the magnetic properties of strongly correlated d, f- electrons, spin and orbital magnetic susceptibilities, magnetic, electronic and phonon contributions to the temperature dependences of heat capacity and thermal expansion. We will construct phase diagrams of spin states in the coordinates pressure – temperature, and the intensity of the external magnetic field – temperature