Symbols and Constants ix Chapter 1. General Relativity 1Brahim LAMINE 1.1. The fundamentals of general relativity 1 1.2. Tensor analysis and curvature of space-time 33 1.3. General relativity equations 68 1.4. References 104 Chapter 2. Compact Objects 107Natalie WEBB 2.1. Introduction 107 2.2. White dwarfs 109 2.3. Neutron stars 120 2.4. Black holes 140 2.5. Binary systems 153 2.6. References 170 Chapter 3. Gravitational Waves 179Patrice HELLO 3.1. Gravitational waves in the context of general relativity 179 3.2. Detection of gravitational waves 201 3.3. Gravitational wave astronomy 227 3.4. The future 249 3.5. References 249 Chapter 4. The Friedmann-Lemaître Universe and Cosmological Expansion 253Richard TAILLET 4.1. Geometry 254 4.2. Cosmological expansion 261 4.3. The Friedmann-Lemaitre equations 268 4.4. Temporal evolution 275 4.5. Horizons 294 4.6. Distances 303 4.7. The redshift-luminosity relation 311 4.8. Angular size distance 317 4.9. Cosmological supernovas 321 4.10. Conclusion 332 4.11. References 335 List of Authors 337 Index 339