These proceedings present the technical contributions to the First Conference on Auctions, Market Mechanisms, and Their Applications (AMMA), held May 8-9, 2009 in Boston, Massachusetts, USA. The conference was devoted to issues that arise in all stages of deploying a market mechanism to solve a problem, including theoretical and empirical examinations. In addition to more traditional academic papers, the conf- ence placed emphasis on experiences from the real world, including case studies and new applications. The main goal of AMMA was to explore the synergy required for good mechanism design. This includes an understanding of the economic and game-theoretic issues, the ability to design protocols and algorithms for realizing desired outcomes, and the knowledge of specific institutional details that are important in practical applications. We were lucky enough to attract papers and talks from economists and computer scientists, theorists and empiricists, academics and practitioners. The program, as reflected in these proceedings, ranged from fundamental theory on auctions and m- kets to empirical design and analysis of matching mechanisms, peer-to-peer-systems, and prediction markets.