Yekaterinburg: Ural State University . A. M. 2008 . 152 s. The basis for this textbook was the lectures that were given by the authors for students of the Faculty of Mathematics and Mechanics of the Ural State University .. A. M. Gorky, students in the specialties "Mathematics, Applied Mathematics", "Mathematics, Computer Science" and "Computer Security" . The book presents discrete optimization algorithms on graphs and networks. The material devoted to algorithms contains a fairly strict justification for them. Of course, in the construction and analysis of algorithms, the basic theoretical and graph concepts and facts are used. The selection of topics raised in the book is largely determined by the tastes of the authors. We wanted to introduce a family of discrete optimization algorithms most commonly used by programmers. We sought to cite the main achievements, not stopping at the details and not going into a detailed review of the results on the topics under discussion ..