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Recent developments in unconventional superconductivity theory

The review of recent developments in the unconventional superconductivity theory is given. In the fist part I consider the physical origin of the Kerr rotation polarization of light reflected from the surface of superconducting $Sr_2RuO_4$. Then the comparison of magneto-optical responses in superconductors with orbital and spin spontaneous magnetization is presented. The latter result is applied to the estimation of the magneto-optical properties of neutral superfluids with spontaneous magnetization. The second part is devoted to the natural optical activity or gyrotropy properties of noncentrosymmetric metals in their normal and superconducting states. The temperature behavior of the gyrotropy coefficient is compared with the temperature behavior of paramagnetic susceptibility determining the noticeable increase of the paramagnetic limiting field in noncentrosymmetric superconductors. In the last chapter I describe the order parameter and the symmetry of superconducting state in the itinerant ferromagnet with orthorhombic symmetry. Finally the Josephson coupling between two adjacent ferromagnet superconducting domains is discussed.