This book for the first time unifies the theories of acoustic, electromagnetic, and elastic waves and discusses the many physical and geometric aspects of their interactions with obstacles. It offers a complete introduction to scattering theory, and goes on to discuss low frequency scattering in particular. A significant number of results are previously unpublished, and the book fills many gaps in the existing literature. Included is an extended bibliography covering the whole existing literature on low frequency scattering, making this an invaluable reference for researchers.