The class studies different mechanisms to allocate a scarce resource, frequently called markets, using theoretical models. We will cover centralized markets, which clear via a single price, waiting or rationing, or use centralized algorithms to allocate demand and supply; decentralized markets, which clear via search; and auction markets. In each case, we will study how market rules determine the incentives of market participant and how to design these markets, focusing on efficiency and revenue maximization. Applications to electricity markets, concert tickets, ride-sharing, labor markets, school choice, dating markets, sponsored search ad auctions, and spectrum auctions will be covered.