Abstract: The central goal of the rapidly developing field of spintronics is to create and control the spin polarization of electrons in solids. A particularly promising direction for achieving this goal involves the use of antiferromagnets (AFMs) due to the absence of stray fields in the AFM compounds. In the present lecture we report a theoretical study of magnetically-induced Pekar- Rashba spin splitting in antiferromagnetic bulk crystals [1,2] and monolayers [2,3] of both nonlayered crystals MnF2 , MnO2 and layered crystals MnPS3. A detailed two-step procedure for determining magnetic layer group of a given monolayer is described, and all the magnetic layer groups into seven spin splitting prototypes are classified.. The latter classification allows one to determine on the basis of symmetry arguments whether spin splitting is prohibited or allowed in a given monolayer. In the latter case, the magnitude of spin splitting can be determined from Density Functional Theory calculations. The above procedure is implemented using both layered (MnPS3) and nonlayered (MnO2) crystals as illustrative examples. For the layered crystals a unique set of Miller indices specifies the monolayer, while in the latter case the most energetically favorable monolayer needs to be determined from DFT calculations. REFERENCES: 1. L. D. Yuan, Z. Wang, J. W. Luo, and A. Zunger, Phys. Rev. Mat. 5, 014409 (2021) 2 S. A. Egorov and R. A. Evarestov, J. Phys. Chem. Lett. 12, 2363 (2021) 3. S. A. Egorov, D. B. Litvin, and R. A. Evarestov, J. Phys. Chem. C submitted, (2021) 4. D. B. Litvin, Magnetic Group Tables (International Union of Crystallography: 2013).