Many X-Ray Free-Electron Lasers (X-FELs) have been designed, built and commissioned since the first lasing of the Linac Coherent Light Source in the hard and soft X-ray regions, and great progress has been made in improving their performance and extending their capabilities. Meanwhile, experimental techniques to exploit the unique properties of X-FELs to explore atomic and molecular systems of interest to physics, chemistry, biology and the material sciences have also been developed. As a result, our knowledge of atomic and molecular science has been greatly extended. Nevertheless, there is still much to be accomplished, and the potential for discovery with X-FELs is still largely unexplored. The next generation of scientists will need to be well versed in both particle beams/FEL physics and X-ray photon science. This book presents material from the Enrico Fermi summer school: Physics of and Science with X-Ray Free-Electron Lasers, held at the Enrico Fermi International School of Physics in Varenna, Italy, from 26 June - 1 July 2017. The lectures presented at the school were aimed at introducing graduate students and young scientists to this fast growing and exciting scientific area, and subjects covered include basic accelerator and FEL physics, as well as an introduction to the main research topics in X-FEL-based biology, atomic molecular optical science, material sciences, high-energy density physics and chemistry. Bridging the gap between accelerator/FEL physicists and scientists from other disciplines, the book will be of interest to all those working in the field.