This textbook is prepared on the basis of the author’s onesemester lecture notes reflecting the Mathematical Logic course for undergraduate and graduate students of mathematical or applied mathematical departments.

This book is a compact introduction to many of the important topics of classical mathematical logic, comprising natural and unrestricted theoretic methods. It covers propositional logic, predicate calculus, and axiomatic arithmetic. The major results of Gödel about the incompleteness of formal systems are also given in an adapted version.

The textbook also contains many exercises, which can be used for practical tasks and exams. This book should be of interest to introductory courses for students of mathematics, philosophy, computer science, and electrical engineering.

I believe that the essential parts of the book can be read with ease by anyone with some experience in abstract mathematical thinking. There is, however, no specific prerequisite, but some knowledge of Boolean functions, set theory, and algorithm theory can be useful.