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Optimization models play an increasingly important role in ¯nancial de- cisions. Many computational ¯nance problems ranging from asset allocation to risk management, from option pricing to model calibration can be solved e±ciently using modern optimization techniques. This course discusses sev- eral classes of optimization problems (including linear, quadratic, integer, dynamic, stochastic, conic, and robust programming) encountered in ¯nan- cial models. For each problem class, after introducing the relevant theory (optimality conditions, duality, etc.) and e±cient solution methods, we dis- cuss several problems of mathematical ¯nance that can be modeled within this problem class. In addition to classical and well-known models such as Markowitz' mean-variance optimization model we present some newer optimization models for a variety of ¯nancial problems.