  In Chapter 1 we start with general Landau scheme of the conservation laws for
the hydrodynamics of classical liquids and superfluids. On the basis of Landau
scheme we consider hydrodynamics of rotating superfluids with large number of
vortices. We study different regimes of slow and fast rotations. In Chapter 4
we consider complicated and yet unresolved problem of chiral anomaly in
superfluid 3He-A and present two competing approaches. The first one is based
on supersymmetric hydrodynamics, another one on the formal analogy with Dirac
equation in QED. In Chapters 6 and 7 we study composed fermions and bosons
which correspond to the different bound states consisting of two fermions, two
bosons and fermion and boson in ultracold quantum gasses and mixtures. We also
elucidate the exact solutions of the Skorniakov-Ter-Martirosian integral
equations. We present the basic ideas of Nozieres-Schmitt Rink and Legget
theory on BCS-BEC crossover in quantum gasses and construct the phase diagrams
for the s-wave and p-wave pairings. In Chapters 9 and 10 we discuss non-phonon
mechanisms of superconductivity of the Kohn-Luttinger type for different models
in 3D and 2D electron systems at low densities including Fermi-gas, Hubbard and
Shubin-Vonsovsky models. We complete the superconductive phase-diagrams of
p-wave and d-wave pairing and discuss the possibility to increase Tc already at
low density. In Chapters 15 and 16 the mechanisms of electron nanoscale
phase-separation in manganite-type oxide materials are analyzed. The
instability of magnetic (or charge) homogeneous ordering towards the formation
of droplet structures (magnetic polarons) is predicted for a wide parameter
range on the phase-diagram. The transport properties of these materials in the
phase-separated state are also discussed.
