Valeria Ferrari is Professor of Theoretical Physics at Sapienza University of Rome (Italy), now retired. She has been Director of the Doctoral School in Physics of Sapienza, chaired the Virgo-EGO Scientific Forum and co-chaired the European Research Network COST Action GWverse. She has been a member of the Editorial Board of several international journals and of the Board of the International Society of General Relativity and Gravitation. She is a founding member of the Amaldi Research Center for Gravitational Physics at Sapienza. For more than forty years her research focused on black hole and stellar perturbations, and on gravitational wave sources.Leonardo Gualtieri is Professor of Theoretical Physics at University of Pisa (Italy). He is a member of the Board of the International Society of General Relativity and Gravitation and has been the coordinator of TEONGRAV, the INFN network of Italian groups studying gravitational wave sources. He works in the field of gravitational theory and phenomenology, with special focus on gravitational wave sources as probes of fundamental physics.Paolo Pani is Professor of Theoretical Physics at Sapienza University of Rome (Italy) and Senior Fellow at Sapienza’s School for Advanced Studies. He received the SIGRAV Prize from the Italian Society of General Relativity and Gravitational Physics for his studies on black hole physics and gravitational wave phenomenology, and their connections to fundamental physics.

• 1. Introduction 2. Elements of Differential Geometry 3. Affine Connection and Parallel Transport 4. The Curvature Tensor 5. The Stress-Energy Tensor 6. The Einstein Equations 7. Einstein’s Equations and Variational Principles 8. Symmetries 9. The Schwarzschild Solution 10. Geodesic Motion in Schwarzschild’s Spacetime 11. Kinematical Tests of General Relativity 12. Gravitational Waves 13. Gravitational Waves in the Quadrupole Approximation 14. Gravitational Wave Sources 15. Gravitational Waves from Oscillating Black Holes 16. Compact Stars 17. The Far-Field Limit of an Isolated Object 18. The Kerr Solution 19. Geodesic Motion in Kerr’s Spacetime 20. Black Hole Thermodynamics

"The book is an excellent starting point for students interested in gravitational wave astronomy and relativistic astrophysics, introducing the reader to exciting recent developments, such as the first LIGO/Virgo observations of gravitational waves from the mergers of black holes and neutron stars. The choice of material is well-balanced and it includes important topics which are not usually covered in detail in introductory textbooks, such as black hole perturbation theory and geodesic motion in the Kerr spacetime." — Dr. Emanuele Berti, Professor, Johns Hopkins University, USA

Valeria Ferrari is Professor of Theoretical Physics at Sapienza University of Rome (Italy), now retired. She has been Director of the Doctoral School in Physics of Sapienza, chaired the Virgo-EGO Scientific Forum and co-chaired the European Research Network COST Action GWverse. She has been a member of the Editorial Board of several international journals and of the Board of the International Society of General Relativity and Gravitation. She is a founding member of the Amaldi Research Center for Gravitational Physics at Sapienza. For more than forty years her research focused on black hole and stellar perturbations, and on gravitational wave sources.Leonardo Gualtieri is Professor of Theoretical Physics at University of Pisa (Italy). He is a member of the Board of the International Society of General Relativity and Gravitation and has been the coordinator of TEONGRAV, the INFN network of Italian groups studying gravitational wave sources. He works in the field of gravitational theory and phenomenology, with special focus on gravitational wave sources as probes of fundamental physics.Paolo Pani is Professor of Theoretical Physics at Sapienza University of Rome (Italy) and Senior Fellow at Sapienza’s School for Advanced Studies. He received the SIGRAV Prize from the Italian Society of General Relativity and Gravitational Physics for his studies on black hole physics and gravitational wave phenomenology, and their connections to fundamental physics.

• 1. Introduction 2. Elements of Differential Geometry 3. Affine Connection and Parallel Transport 4. The Curvature Tensor 5. The Stress-Energy Tensor 6. The Einstein Equations 7. Einstein’s Equations and Variational Principles 8. Symmetries 9. The Schwarzschild Solution 10. Geodesic Motion in Schwarzschild’s Spacetime 11. Kinematical Tests of General Relativity 12. Gravitational Waves 13. Gravitational Waves in the Quadrupole Approximation 14. Gravitational Wave Sources 15. Gravitational Waves from Oscillating Black Holes 16. Compact Stars 17. The Far-Field Limit of an Isolated Object 18. The Kerr Solution 19. Geodesic Motion in Kerr’s Spacetime 20. Black Hole Thermodynamics

"The book is an excellent starting point for students interested in gravitational wave astronomy and relativistic astrophysics, introducing the reader to exciting recent developments, such as the first LIGO/Virgo observations of gravitational waves from the mergers of black holes and neutron stars. The choice of material is well-balanced and it includes important topics which are not usually covered in detail in introductory textbooks, such as black hole perturbation theory and geodesic motion in the Kerr spacetime." — Dr. Emanuele Berti, Professor, Johns Hopkins University, USA

Valeria Ferrari is Professor of Theoretical Physics at Sapienza University of Rome (Italy), now retired. She has been Director of the Doctoral School in Physics of Sapienza, chaired the Virgo-EGO Scientific Forum and co-chaired the European Research Network COST Action GWverse. She has been a member of the Editorial Board of several international journals and of the Board of the International Society of General Relativity and Gravitation. She is a founding member of the Amaldi Research Center for Gravitational Physics at Sapienza. For more than forty years her research focused on black hole and stellar perturbations, and on gravitational wave sources.Leonardo Gualtieri is Professor of Theoretical Physics at University of Pisa (Italy). He is a member of the Board of the International Society of General Relativity and Gravitation and has been the coordinator of TEONGRAV, the INFN network of Italian groups studying gravitational wave sources. He works in the field of gravitational theory and phenomenology, with special focus on gravitational wave sources as probes of fundamental physics.Paolo Pani is Professor of Theoretical Physics at Sapienza University of Rome (Italy) and Senior Fellow at Sapienza’s School for Advanced Studies. He received the SIGRAV Prize from the Italian Society of General Relativity and Gravitational Physics for his studies on black hole physics and gravitational wave phenomenology, and their connections to fundamental physics.

• 1. Introduction 2. Elements of Differential Geometry 3. Affine Connection and Parallel Transport 4. The Curvature Tensor 5. The Stress-Energy Tensor 6. The Einstein Equations 7. Einstein’s Equations and Variational Principles 8. Symmetries 9. The Schwarzschild Solution 10. Geodesic Motion in Schwarzschild’s Spacetime 11. Kinematical Tests of General Relativity 12. Gravitational Waves 13. Gravitational Waves in the Quadrupole Approximation 14. Gravitational Wave Sources 15. Gravitational Waves from Oscillating Black Holes 16. Compact Stars 17. The Far-Field Limit of an Isolated Object 18. The Kerr Solution 19. Geodesic Motion in Kerr’s Spacetime 20. Black Hole Thermodynamics

"The book is an excellent starting point for students interested in gravitational wave astronomy and relativistic astrophysics, introducing the reader to exciting recent developments, such as the first LIGO/Virgo observations of gravitational waves from the mergers of black holes and neutron stars. The choice of material is well-balanced and it includes important topics which are not usually covered in detail in introductory textbooks, such as black hole perturbation theory and geodesic motion in the Kerr spacetime." — Dr. Emanuele Berti, Professor, Johns Hopkins University, USA