The book is based on the materials of lectures and seminars conducted by the authors for junior students of the Mechanics and Mathematics Department of Moscow State University. It tells about the basic concepts of mathematical logic (logic of statements, first-order languages, expressiveness, calculus of statements, solvable theories, completeness theorem, principles of model theory). The presentation is designed for students of mathematical schools, mathematics students and everyone interested in mathematical logic. The book includes about 200 tasks of various difficulties.