Atomic correlations have been studied in physics for over 50 years and known as collective effects until recently when they came to be recognized as a source of entanglement. This is the first book that contains detailed and comprehensive analysis of two currently extensively studied subjects of atomic and quantum physics—atomic correlations and their relations to entanglement between atoms or atomic systems—along with the newest developments in these fields. This book assembles accounts of many phenomena related to or resulting from atomic correlations. The essential language of the book is in terms of density matrices and master equations that provide detailed theoretical treatments and experimental analysis of phenomena such as entanglement between atoms, spontaneously or externally induced atomic coherence, engineering of atomic correlations, storage and controlled transfer of correlations, and dynamics of correlated systems.