This text discusses the physical principles of how and why crystals grow. It introduces the fundamental properties of crystal surfaces at equilibrium, and describes simple models and basic concepts of crystal growth including diffusion, thermal smoothing of a surface, and applications to semiconductors. It also covers more complex topics such as kinetic roughness, growth instabilities, and elastic effects, as well as the crucial contributions of crystal growth in electronics during this century. The book focuses on growth using molecular beam epitaxy. Throughout, the emphasis is on the role played by modern statistical physics. Informative appendices, interesting exercises and an extensive bibliography reinforce the text.