1. Introduction -- 2. Crystal Structure -- 3. Antiferromagnetism in Cuprate Superconductors -- 4. Thermodynamic Properties of Cuprate Superconductors -- 5. Electronic Properties of Cuprate Superconductors -- 6. Lattice Dynamics and Electron-Phonon Interaction -- 7. Theoretical Models of High-Tc Superconductivity -- 8. Applications -- 8.3 Conclusion -- Thermodynamic Green Functions in Superconductivity -- Theory A.1 Thermodynamic Green Functions -- A.1.1 Green Function Definition -- A.1.2 Spectral Representation -- A.1.3 Sum Rules and Symmetry Relations -- A.2 Eliashberg Equations for Fermion-Boson Models -- A.2.1 Dyson Equation -- A.2.2 Non-Crossing Approximation -- A.3 Superconductivity in the Hubbard Model -- A.3.1 Dyson Equation -- A.3.2 Mean-Field Approximation -- A.3.3 Self-energy Operator -- A.4 Superconductivity in the t-J Model -- References.

High-Temperature Cuprate Superconductors provides an up-to-date and comprehensive review of the properties of these fascinating materials. The essential properties of high-temperature cuprate superconductors are reviewed on the background of their theoretical interpretation. The experimental results for structural, magnetic, thermal, electric, optical and lattice properties of various cuprate superconductors are presented with respect to relevant theoretical models. A critical comparison of various theoretical models involving strong electron correlations, antiferromagnetic spin fluctuations, phonons and excitons provides a background for understanding of the mechanism of high-temperature superconductivity. Recent achievements in their applications are also reviewed. A large number of illustrations and tables gives valuable information for specialists. A text-book level presentation with formulation of a general theory of strong-coupling superconductivity will help students and researches to consolidate their knowledge of this remarkable class of materials.