This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include  unconstrained  optimization: optimality conditions, Newton's method, quasi-Newton's methods, Steepest Descent Method, Conjugate-Gradient methods, Line Search methods, Trust Region Methods,  Derivative-Free Methods, constrained Optimization: optimality conditions for (a) linear equality constraints, (b) linear inequality constraints, (c) nonlinear constraints, feasible-point methods, sequential quadratic programming (SQP), reduced-gradient method, penalty and barrier methods.