Basic properties of 4 He and 3He, liquifaction of 4He, Fermi-Dirac and Bose - Einstein quantum statistics. Ideal Bose gas, Bose - Einstein condensation (BEC). Ideal Fermi gas, Fermi liquid, zero sound. Phase diagrams of 4He a 3He, zero oscillations. 3He-4He mixtures, dilution refrigerator.

Superfluid He II - Fountain effect, mechano-caloric effect. Andronikashvili experiment, two-fluid model and Landau equations of motion, energy spectrum, criterion of superfluidity. Superfluid film. Collective modes - first, second, third and fourth sounds. Macroscopic wave function, quantization of circulation - quantized vortices, mutual friction, Kelvin and Tkachenko waves, introduction into superfluid hydrodynamics, superfluid turbulence. Positive and negative ions, ionic mobility, two-dimensional pools of ions below the surface of superfluid helium, plasma oscillations, crystallization.

Superfluid 3He - basic ideas of generalized BCS theory, paramagnons, equal spin pairing, order parameter for the A, B, and A1 phases. Textures and orienting forces, solitons. Nuclear magnetic resonance. Phase-slips and Josephson phenomena in 3He. Rotating 3He- continuous and singular vortices. Superfluid hydrodynamics in 3He, Kelvin-Helmholtz instability, transition to superfluid turbulence. Relationship between superfluidity and cosmology, Kibble-Zurek mechanism.

BEC - hydrogen, alcali atoms, experiments, principles of laser cooling, BEC and superfluidity. Quantized vortices in BEC.

Phase diagrams and basic properties of 4 He and 3He. Superfluid He II- two fluid model, collective modes, fountain effect, superfluid film, energy spectrum, macroscopic wave function, quantization of circulation- quantized vortices, superfluid hydrodynamics and turbulence.

Superfluid 3He - basic ideas of generalized BCS theory, order parameter for the A, B and A1 phases, textures, orienting forces, NMR, phase-slips and Josephson phenomena in 3He, rotating 3He-continuous and singular vortices. BEC - hydrogen, alcali atoms, experiments, principles of laser cooling, BEC and superfluidity.