This book generalizes earlier theories of belief change to cover all kinds of changes of sets by sets. The principal focus is still on changes of belief sets in response to new evidence. But the formal theory extends to all domains with a closure operation and a preference structure, including, for example, systems of action. Contraction is the key notion; all other changes can be defined. Various new applications of the theory are outlined. A sentential version of contraction, subtraction, is proposed as a formal counterpart to "except"-locutions in natural language. Connections are emphasized with other areas at the interface between philosophical logic and artificial intelligence such as reasoning form default assumptions or from inconsistent premises.