The objective of this research is to design daily electricity markets for efficiency, incentive compatibility, robustness, and smart grid considerations. The approach is to first establish economic foundations of electricity auctions through effective use of the extended optimality conditions for mixed-integer problems and the introduction of the novel ?local incentive compatibility? concept. The theory will be substantiated on a few promising auction models for equilibrium, incentive compatibility, efficiency, revenue balance, and practicality in implementation. The results will then be extended to stochastic formulations to accommodate intermittent and uncertain renewable generation, and to make effective use of smart metering infrastructure for market-based demand response through innovative integration of stochastic programming, Lagrangian relaxation, and stochastic dynamic programming. The intellectual merits include a new perspective to look at electricity markets; substantiate the results on promising models based on a synergistic integration of latest results from mathematics, economics, and our insights on markets; and the novel approach to formulate and solve stochastic auction problems. The proposed research shall have the broader impacts of enabling the research, development, and policy-making communities to assess the merits of key auction mechanisms to realize green and robust electricity markets. It will also contribute to auction theory and practice of other fields with similar characteristics, e.g., natural gas and supply chain. Finally, the research will educate graduate/undergraduate students and professionals through research, courses, seminars, online materials, CD/DVD offerings, and UConn?s da Vinci program for high school teachers and counselors. The participations of under-represented groups will be actively sought.