The Book of Mathematics . Elements of mathematical logic: guidelines for the preparation of bachelors in the direction of 220400 (27.) 03. 04)”, created by a team of authors, is an indispensable educational resource for students mastering the basics of logic and mathematical thinking within higher education. This book is not just a collection of theoretical positions, but a lively and fascinating journey into the world of logical structures, formal systems and methods of proof, which reveals to the reader the deep mechanisms of mathematical thinking. What makes this manual especially valuable? First, it is carefully structured to help students understand complex concepts of mathematical logic without unnecessary confusion and excessive abstraction. It discusses in detail the basic elements of logic, such as logical operations, statement calculus, predicate logic, and methods for constructing logical proofs. The author's team, possessing rich pedagogical and scientific experience, skillfully combines theory with practical tasks, which allows students to consolidate the material and develop analytical skills. This book is ideal for undergraduate students studying in the direction of 220400 "Mathematics and Mechanics" or related disciplines, as well as those who are interested in the theoretical foundations of computer science, logic and mathematical analysis. It will be useful both for beginners and for those who already have basic knowledge and want to deepen their knowledge in the field of logic, formal systems and methods of proof. Especially valuable will be a manual for those who are preparing for exams, writing term papers and diploma papers, as well as for teachers looking for modern and structured material for training sessions. The peculiarity of the book is not only a systematic approach to the presentation of material, but also a special style of authors combining clarity of presentation with academic rigor. It traces the author's manner of presentation, which helps students not only to understand, but also to love mathematics and logic as the fundamental sciences underlying modern information technology and scientific research. The book raises the most important topics, such as formal languages, proof theories, logical conclusions and their application in computer science, which makes it relevant and in demand in the context of modern scientific progress. In addition, the book "Mathematics . Elements of Mathematical Logic” is not only a textbook, but also a source of inspiration for those who want to understand how logical systems work, how evidence is built and why mathematics is the language spoken by modern science. The reader will find here many examples, tasks and exercises that help to consolidate theoretical knowledge and develop critical thinking. This approach makes the book especially attractive for those who appreciate the practical application of the theory and want to learn how to think logically and systematically. If you are looking for a book that will help you understand the basics of mathematical logic, expand your knowledge and prepare for academic challenges, "Mathematics. Elements of mathematical logic” will become your reliable companion This publication is the result of the work of experienced teachers and scientists, which deservedly takes its place in the library of each student seeking a deep understanding of the mathematical foundations and the development of analytical thinking. In today's world, where logic and formal systems play a key role in information technology, artificial intelligence and scientific research, this book opens up new horizons and helps you understand complex ideas in simple and accessible language.