The mechanics of earthquake faulting is a multi-disciplinary scientific approach combining laboratory inferences and mathematical models with the analysis of recorded data from earthquakes, and is essential to the understanding of these potentially destructive events. The modern field of study can be said to have begun with the seminal papers by B. V. Kostrov in 1964 and 1966. This book presents lectures delivered at the summer school 'The Mechanics of Earthquake Faulting', held under the umbrella of the Enrico Fermi International School of Physics in Varenna, Italy, from 2 to 7 July 2018. The school was attended by speakers and participants from many countries. One of the most important goals of the school was to present the state-of-the-art of the physics of earthquakes, and the 10 lectures included here cover the most challenging aspects of the mechanics of faulting. The topics covered during the school give a very clear picture of the current state of the art of the physics of earthquake ruptures and also highlight the open issues and questions that are still under debate, and the book will be of interest to all those working in the field.