The module provides basic knowledge of mathematical logic and its applications in computer science. Students learn the mathematical foundations of logical thinking and reasoning and develop formalizations of tasks, problems and structures in computer science in the language of logic (primarily predicate logic). Propositional logic: syntax and semantics; Horn formulas; resolution; calculus of natural inference; syntax and semantics of 1st level predicate logic; formalization, axiomatization and theories; Gödel's completeness theorem; finiteness theorem; Löwenheim-Skolem theorems; modal logic; 2nd level logic.