The proposed textbook forms the basis of a set on the course of mathematical logic and theory of algorithms, which also includes a collection of problems (Igoshin V.I. Tasks and exercises on mathematical logic and theory of algorithms). The basics of the theory are described in detail, the directions of logic penetration into the foundations of algebra, analysis, geometry are shown, the material of the school course of mathematics for its logical analysis is involved, the relationship of mathematical logic with computers, computer science, and artificial intelligence systems is characterized. For students of universities, technical and pedagogical universities studying in the specialties "Mathematics," "Applied Mathematics."