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In optimal auction design literature, it is a common assumption that valuations of buyers are independently drawn from a unique distribution. In this thesis, we study auctions with ambiguity for an environment where valuation distribution is uncertain itself and introduce a linear programming approach to robust auction design problem. We develop an algorithm that gives the optimal solution to the problem under certain assumptions when the seller is ambiguity averse with prior set P and the buyers are ambiguity neutral with a prior f in P. Also, we consider the case where the buyers are ambiguity averse as the seller and formulate this problem as a mixed integer programming problem. Then, we propose a hybrid algorithm that enables to achieve a good solution for this problem in a reduced time.