The training guide is devoted to the presentation of the foundations of discrete mathematics. The main sections are presented: theories of sets, mathematical logic, relations, formal systems, algorithms, algebras, combinatorics, graphs, fractal sets. The theoretical material is illustrated by a large number of examples. The guide includes not only basic concepts and theoretical results, but also methods and algorithms for solving applied tasks. Addressed primarily to teachers and students of higher technical universities, but it can be useful to those who are wish to study it independently. With this goal, a large number of tasks are included, for the knowledge control and the system of assessing them. In each section there are two-level test tasks. The first level – tests to check the compulsory minimum of knowledge, the second – tasks of full complexity. The historical information about scientists who contributed to the development of discrete mathematics is given.