Textbook in PDF format This introductory text is based on courses within a multi-semester cycle on “Numerical Mathematics” given by the author at the Universities in Saarbrücken and Heidelberg. In the present part basic concepts of numerical methods are presented for solving linear optimization problems (so-called “Linear Programming”). This includes besides the classical ”Simplex method“ also modern ”Interior-point methods“. As natural extensions methods for convex nonlinear, especially quadratic, optimization problems are discussed. Theoretical as well as practical aspects are considered. As prerequisite only that prior knowledge is required, which is usually taught in the introductory Analysis, Linear Algebra, and Numerics courses. For facilitating self-learning the book contains theoretical and practical exercises with solutions collected in the appendix