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In Chapter 1 we start with general Landau scheme of the conservation laws forthe hydrodynamics of classical liquids and superfluids. On the basis of Landauscheme we consider hydrodynamics of rotating superfluids with large number ofvortices. We study different regimes of slow and fast rotations. In Chapter 4we consider complicated and yet unresolved problem of chiral anomaly insuperfluid 3He-A and present two competing approaches. The first one is basedon supersymmetric hydrodynamics, another one on the formal analogy with Diracequation in QED. In Chapters 6 and 7 we study composed fermions and bosonswhich correspond to the different bound states consisting of two fermions, twobosons and fermion and boson in ultracold quantum gasses and mixtures. We alsoelucidate the exact solutions of the Skorniakov-Ter-Martirosian integralequations. We present the basic ideas of Nozieres-Schmitt Rink and Leggettheory on BCS-BEC crossover in quantum gasses and construct the phase diagramsfor the s-wave and p-wave pairings. In Chapters 9 and 10 we discuss non-phononmechanisms of superconductivity of the Kohn-Luttinger type for different modelsin 3D and 2D electron systems at low densities including Fermi-gas, Hubbard andShubin-Vonsovsky models. We complete the superconductive phase-diagrams ofp-wave and d-wave pairing and discuss the possibility to increase Tc already atlow density. In Chapters 15 and 16 the mechanisms of electron nanoscalephase-separation in manganite-type oxide materials are analyzed. Theinstability of magnetic (or charge) homogeneous ordering towards the formationof droplet structures (magnetic polarons) is predicted for a wide parameterrange on the phase-diagram. The transport properties of these materials in thephase-separated state are also discussed.

Modern trends in Superconductivity and Superfluidity. Selected Chapters