This text outlines the application of auction methods for all aspects of power system operation, primarily for a competitive environment. A complete description of the industry structure, as well as the various markets is given. A thorough introduction to auction basics is included to explain how auctions have grown in other industries. Auction methods are compared to classical techniques for power system analysis, operations, and planning. The traditional applications of economic dispatch, optimal power flow and unit commitment are compared to auction mechanisms. Algorithms for auctions using linearized power flow equations, DC power flow equations, and AC power flow equations are included. The bundling of supportive services, known as ancillary services within the United States, is discussed. Extensions to the basic auction algorithms for inclusion of supportive services, as well as algorithms for scheduling and bidding on generation for GENCOs or independent power producers are presented. It provides an introduction to how electricity will be traded as a commodity in the future.