A book of famous American mathematicians, which is currently one of the most famous books on mathematical logic in the USA, which has survived three editions there (1974, 1980, 1989). It contains the beginnings and some additional chapters of mathematical logic, consistently and strictly sets out the classical theorems on the insolubility of predicate logic and the solvability of some of its fragments, the famous Gödel theorems on completeness, non-standard models and much more. The material is supplemented with exercises.