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