Linear programming (simplex method, duality theory, sensitivity analysis, interior point methods, decomposition method), the theory of polyhedra (definition and dimension of polyhedra, the description of polyhedra using section, a description of polyhedra using points and extreme rays, polarity, polyhedra connection between linear and integer programs ), integer programming (theory of valid inequalities, valid inequalities for 0-1 knapsack polytope, valid inequalities for symmetric polytope of a traveling salesman, the Lagrangian relaxation and duality, branching and limiting using relaxation linear programming, generalized algorithms of cross-sectional plane).