This book describes collisions between atoms that have been cooled to extremely low temperatures by optical and evaporative cooling techniques. John Weiner reviews the elements of the quantum theory of scattering, and summarizes the theory and experimental techniques of optical cooling and trapping. He also describes applications to precision spectroscopy, the determination of atomic properties, control of inelastic collisions by laser fields, and the manipulation of Bose-Einstein condensates (mesoscopic quantum systems).