A synthesis of theoretical and practical research on combinatorial auctions from the perspectives of economics, operations research, and computer science. The study of combinatorial auctions - auctions in which bidders can bid on combinations of items or packages - draws on the disciplines of economics, operations research, and computer science. This landmark collection integrates these three perspectives, offering a state-of-the art survey of developments in combinatorial auction theory and practice by leaders in the field. Combinatorial auctions (CAs), by allowing bidders to express their preferences more fully, can lead to improved economic efficiency and greater auction revenues. However, challenges arise in both design and implementation. Combinatorial Auctions addresses each of these challenges. After describing and analysing various CA mechanisms, the book addresses bidding languages and questions of efficiency. Possible strategies for solving the computationally intractable problem of how to compute the objective- maximising allocation (known as the winner determination problem) are considered, as are questions of how to test alternative algorithms. The book discusses five important applications of CAs: spectrum auctions, airport takeoff and landing slots, procurement of freight transportation services, the London bus routes market, and industrial procurement. This unique collection makes recent work in CAs available to a broad audience of researchers and practitioners. The integration of work from the three disciplines underlying CAs, using a common language throughout, serves to advance the field in theory and practice.