I Basic Concepts. - 1 Introduction: Brief History of Black Hole Physics. - 2 Spherically Symmetric Black Holes. - 3 Rotating Black Holes. - 4 Black hole Perturbations (Written jointly with N. Andersson). - 5 General Properties of Black Holes. - 6 Stationary Black Holes. - 7 Physical Effects in the Gravitational Field of a Black Hole. - 8 Black Hole Electrodynamics. - >9 Astrophysics of Black Holes. - II Further Developments. - 10 Quantum Particle Creation by Black Holes. - 11 Quantum Physics of Black Holes. - 12 Thermodynamics of Black Holes. - 13 Black Holes in Unified Theories. - 14 The Interior of a Black Hole. - 15 Ultimate Fate of Black and White Holes. - 16 Black Holes Wormholes and Time Machines. - Conclusion. - Appendices. - A Mathematical Formulas. - A. 1 Differential Manifold. Tensors. - A. 2 Metric. Space and Time Intervals. - A. 3 Causal Structure. - A. 4 Covariant Derivative. - A. 5 Geodesic Lines. - A. 6 Curvature. - A. 7 Lie- and Fermi-Transport. - A. 8 Symmetries and Conservation Laws. - A. 9 Geometry of Congruence of Lines. - A. 10 Stationary Congruences. - A. 10. 1 Killing congruence. - A. 10. 2 Congruence of locally non-rotating observers. - A. 11 Local Reference Frames. - A. 12 Geometry of Subspaces. - A. 13 Integration in Curved Space. - A. 14 Conformai Transformations. - A. 15 Einstein Equations. - B Spherically Symmetric Spacetimes. - B. 1 Spherically Symmetric Geometry. - B. 2 Reduced Action. - B. 3 Generalized Birkhoff's Theorem. - B. 4 Spherically Symmetric Vacuum Solutions. - B. 4. 1 Schwarzschild metric. - B. 4. 2 Scaling properties. - B. 5 Kruskal Metric. - B. 5. 1 Derivation of Kruskal metric. - B. 5. 2 Relation between Kruskal and Schwarzschild metrics. - B. 5. 3 Kruskal spacetime as maximal analytical continuation of the Schwarzschild metric. - B. 5. 4 Einstein-Rosen bridge. - B. 6 Tolman Solution. - C Rindler Frame inMinkowski Spacetime. - C. 1 Uniformly Accelerated Motion. - C. 2 Rindler Frame. - C. 3 Light and Particle Propagation. - C. 4 Maximal Analytical Extension of Rindler Spacetime. - D Kerr-Newman Geometry. - D. 1 Kerr-Newman Metric. - D. 2 Christoffel Symbol. - D. 3 Symmetries. - D. 4 Motion of Test Particles. - D. 4. 1 Integrals of motion. - D. 4. 2 Hamilton-Jacobi method. - D. 5 Stationary Congruences in the Kerr-Newman Geometry. - D. 5. 1 Killing congruence. - D. 5. 2 Congruence of locally non-rotating observers. - D. 6 Algebraic Properties. - D. 7 Analytic Extension. - E Newman-Penrose Formalism. - E. 1 Complex Null Tetrad. Spin Coefficients. - E. 2 Covariant Derivatives. Ricci and Weyl Tensor. - E. 3 Newman-Penrose Equations. - E. 4 Bianchi Identities. - F Wave Fields in a Curved Spacetime. - F. 1 Scalar Field. - F. 2 Electromagnetic Field. - F. 3 Gravitational Perturbations. - G Wave Fields in the Kerr Metric. - G. 1 Teukolsky Equation. - G. 2 Separation of Variables. Spin-Weighted Spheroidal Harmonics. - G. 3 Radial Equation. - G. 4 Massless Scalar Field. - G. 5 Electromagnetic Field. - G. 6 Gravitational Perturbations. - H Quantum Fields in Kerr Spacetime. - H. 1 Quantum Theory in an External Field. - H. 2 Vacuum. Many-Particle States. - H. 4 Massless Fields Quantization in Kerr Spacetime. - H. 6 Averaging over Non-observable States. - I Quantum Oscillator. - 1. 1 Action. - 1. 2 Quantization and Representations. - 1. 3 Quantum Oscillator at Finite Temperature. - 1. 4 Two Mode Coupled Oscillators. Language: English