1.Introduction. 2.Classical optimization unconstrained and equality constrained problems. 3.Optimality conditions for constrained extrema. 4.Convex sets and functions. 5.Duality in nonlinear convex programming. 6.Generalized convexity. 7.Analysis of selected nonlinear programming problems. 8.One- dimensional optimization. 9.Multidimensional unconstrained optimization without derivatives: empirical and conjugate direction methods. 10.Second derivate, steepest descent and conjugate gradient methods. 11.Variable metric algorithmic. 12.Penalty function methods. 13.Solution of constrained problems by extensions of unconstrained optimization techniques. 14.Approximation-type algorithms.