A basic overview of experiments and theory of the integer and fractional quantum Hall effects as well as the main research results on high-temperature superconductors are provided, the main models claiming to describe the attraction mechanism of charge carriers in HTSCs are reviewed. The main physical effects accompanying superfluid phase transitions in helium-3 and helium-4, the difference between phase transitions in a three-dimensional case and in low-dimensional strongly correlated systems, such as superfluid helium in one-dimensional channels, spin chains and ladders, etc., and Bose condensation in alkaline metals, are considered. The material is followed by a review of history of discovery of the effects and bibliographic references when necessary. A sufficiently detailed presentation of theoretical concepts is provided. On selective subjects, problems are discussed with detailed explanations.

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Kashurnikov V. A., Maimistov A.I. Modern problems of solid state physics: Part1. Integer and fractional quantum effects of Hall

Kashurnikov V. A., Krasavin A.V. Modern problems of solid state physics: Part 2. High-temperature superconductivity

Kashurnikov V. A., Krasavin A.V. Modern problems of solid state physics: Part 3. Superfluidity and Bose condensation

Elesin V.F., Kashurnikov V.A. Physics of phase transitions

Kashurnikov V. A., Krasavin A.V. Numerical methods of quantum statistics