Valeria Ferrari is Professor of Theoretical Physics at Sapienza, University of Rome (Italy). She performed research in the fields of General Relativity, with special focus on black hole and stellar perturbations, and gravitational wave sources. She has published over 125 papers in international journals, given over 100 invited talks, in addition to coordinating international research projects, the Virgo-Ego Scientific forum, and serving as part of several journal Editorial Boards. She co-authored textbooks in Physics for undergraduate students.Leonardo Gualtieri is Associate Professor at Sapienza, University of Rome (Italy). His main research interests are gravitational theory and gravitational waves, with special focus on gravitational wave sources as probes of fundamental physics. He has published over 100 papers in international journals and given over 30 invited talks, in addition to coordinating TEONGRAV, the INFN network of Italian groups studying gravitational wave sources.Paolo Pani is Associate Professor of Theoretical Physics at Sapienza, University of Rome (Italy) and Junior Fellow at Sapienza’s School for Advanced Studies. He coordinates the DarkGRA project "Unveiling the dark universe with gravitational waves" funded by the European Research Council (ERC). He received the SIGRAV Prize and the Outstanding Referee award from the American Physics Society. He is co-author of the book “Superradiance” and of over 100 scientific publications 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 Stressenergy Tensor. 6 The Einstein Equations. 7 Einstein’s Equations and Variational Principles. 8 Symmetries. 9 The Schwarzschild Spacetime. 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 Farfield Limit of an Isolated, Stationary Object. 18 The Kerr Solution. 19 Geodesic Motion in Kerr’s Spacetime. 20 Black Hole Thermodynamics

"This textbook introduces the basics of Einstein’s theory of general relativity and of its astrophysical applications. The first half of the book is dedicated to a pedagogical, self-contained treatment of differential geometry. The second half deals with the structure and stability of compact objects (black holes and neutron stars), the classical tests of general relativity, and gravitational waves. 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"At a time when gravitational physics is at the center of many new scientific discoveries, there are many textbooks initiating students to the beauty of General Relativity. Yet, it is hard to find a book that manages so admirably to combine the introductory material with the more advanced topics. Written with skilled perspective of experts who have been teaching these topics for many years, the book provides the novice with a systematic and complete picture of what is arguably the most fascinating theory in physics. At the same time, the book does also offer a detailed account of more advanced and modern topics in relativistic astrophysics such as black holes, compact stars, and gravitational waves. The result is a self-contained and invaluable source for anyone interested in General Relativity. Highly recommended for students and teachers alike."— Prof. Luciano Rezzolla, Institute for Theoretical Physcis, Frankfurt

Valeria Ferrari is Professor of Theoretical Physics at Sapienza, University of Rome (Italy). She performed research in the fields of General Relativity, with special focus on black hole and stellar perturbations, and gravitational wave sources. She has published over 125 papers in international journals, given over 100 invited talks, in addition to coordinating international research projects, the Virgo-Ego Scientific forum, and serving as part of several journal Editorial Boards. She co-authored textbooks in Physics for undergraduate students.Leonardo Gualtieri is Associate Professor at Sapienza, University of Rome (Italy). His main research interests are gravitational theory and gravitational waves, with special focus on gravitational wave sources as probes of fundamental physics. He has published over 100 papers in international journals and given over 30 invited talks, in addition to coordinating TEONGRAV, the INFN network of Italian groups studying gravitational wave sources.Paolo Pani is Associate Professor of Theoretical Physics at Sapienza, University of Rome (Italy) and Junior Fellow at Sapienza’s School for Advanced Studies. He coordinates the DarkGRA project "Unveiling the dark universe with gravitational waves" funded by the European Research Council (ERC). He received the SIGRAV Prize and the Outstanding Referee award from the American Physics Society. He is co-author of the book “Superradiance” and of over 100 scientific publications 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 Stressenergy Tensor. 6 The Einstein Equations. 7 Einstein’s Equations and Variational Principles. 8 Symmetries. 9 The Schwarzschild Spacetime. 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 Farfield Limit of an Isolated, Stationary Object. 18 The Kerr Solution. 19 Geodesic Motion in Kerr’s Spacetime. 20 Black Hole Thermodynamics

"This textbook introduces the basics of Einstein’s theory of general relativity and of its astrophysical applications. The first half of the book is dedicated to a pedagogical, self-contained treatment of differential geometry. The second half deals with the structure and stability of compact objects (black holes and neutron stars), the classical tests of general relativity, and gravitational waves. 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"At a time when gravitational physics is at the center of many new scientific discoveries, there are many textbooks initiating students to the beauty of General Relativity. Yet, it is hard to find a book that manages so admirably to combine the introductory material with the more advanced topics. Written with skilled perspective of experts who have been teaching these topics for many years, the book provides the novice with a systematic and complete picture of what is arguably the most fascinating theory in physics. At the same time, the book does also offer a detailed account of more advanced and modern topics in relativistic astrophysics such as black holes, compact stars, and gravitational waves. The result is a self-contained and invaluable source for anyone interested in General Relativity. Highly recommended for students and teachers alike."— Prof. Luciano Rezzolla, Institute for Theoretical Physcis, Frankfurt

Valeria Ferrari is Professor of Theoretical Physics at Sapienza, University of Rome (Italy). She performed research in the fields of General Relativity, with special focus on black hole and stellar perturbations, and gravitational wave sources. She has published over 125 papers in international journals, given over 100 invited talks, in addition to coordinating international research projects, the Virgo-Ego Scientific forum, and serving as part of several journal Editorial Boards. She co-authored textbooks in Physics for undergraduate students.Leonardo Gualtieri is Associate Professor at Sapienza, University of Rome (Italy). His main research interests are gravitational theory and gravitational waves, with special focus on gravitational wave sources as probes of fundamental physics. He has published over 100 papers in international journals and given over 30 invited talks, in addition to coordinating TEONGRAV, the INFN network of Italian groups studying gravitational wave sources.Paolo Pani is Associate Professor of Theoretical Physics at Sapienza, University of Rome (Italy) and Junior Fellow at Sapienza’s School for Advanced Studies. He coordinates the DarkGRA project "Unveiling the dark universe with gravitational waves" funded by the European Research Council (ERC). He received the SIGRAV Prize and the Outstanding Referee award from the American Physics Society. He is co-author of the book “Superradiance” and of over 100 scientific publications 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 Stressenergy Tensor. 6 The Einstein Equations. 7 Einstein’s Equations and Variational Principles. 8 Symmetries. 9 The Schwarzschild Spacetime. 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 Farfield Limit of an Isolated, Stationary Object. 18 The Kerr Solution. 19 Geodesic Motion in Kerr’s Spacetime. 20 Black Hole Thermodynamics

"This textbook introduces the basics of Einstein’s theory of general relativity and of its astrophysical applications. The first half of the book is dedicated to a pedagogical, self-contained treatment of differential geometry. The second half deals with the structure and stability of compact objects (black holes and neutron stars), the classical tests of general relativity, and gravitational waves. 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"At a time when gravitational physics is at the center of many new scientific discoveries, there are many textbooks initiating students to the beauty of General Relativity. Yet, it is hard to find a book that manages so admirably to combine the introductory material with the more advanced topics. Written with skilled perspective of experts who have been teaching these topics for many years, the book provides the novice with a systematic and complete picture of what is arguably the most fascinating theory in physics. At the same time, the book does also offer a detailed account of more advanced and modern topics in relativistic astrophysics such as black holes, compact stars, and gravitational waves. The result is a self-contained and invaluable source for anyone interested in General Relativity. Highly recommended for students and teachers alike."— Prof. Luciano Rezzolla, Institute for Theoretical Physcis, Frankfurt