This book provides the fundamental statistical theory of atomic transport in crystalline solids, that is the means by which processes occurring at the atomic level are related to macroscopic transport coefficients and other observable quantities. The cornerstones of the authors' treatment are (i) the physical concepts of lattice defects, (ii) the phenomenological description provided by non-equilibrium thermodynamics and (iii) the various methods of statistical mechanics used to link these (kinetic theory, random-walk theory, linear response theory etc.). The book is primarily concerned with transport in the body of crystal lattices and not with transport on surfaces, within grain boundaries or along dislocations, although much of the theory here presented can be applied to these low-dimensional structures when they are atomically well ordered and regular.