1.The nonlinear programming problem, preliminary concepts, and notation. 2.Linear inequalities and theorems of the alternative. 3.Convex sets in Rn. 4.Convex and concave functions. 5.Saddlepoint optimality criteria of nonlinear programming without differentiability. 6.Differentiable convex and concave functions. 7.Optimality criteria in nonlinear programming with differentiability. 8.Duality in Nonlinear programming. 9.Generalizations of convex functions: quasiconvex, strictly quasiconvex, and pseudoconvex functions. 10.Optimality and duality for generalized convex and concave functions. 11.Optimality and duality in the presence of nonlinear equality constraints.