The book "Algebra, the theory of numbers and their applications" by Andrianov A. N. , Borevicha Z. and . and others is a fascinating and deep dive into the world of algebra and number theory. This edition will be a real discovery for students studying mathematics, and for anyone interested in mathematical concepts and their practical applications. The book focuses on the basic principles of algebra and number theory, which the authors consider from different angles, focusing on their relationship and significance in various fields of science and technology. Readers will be able to learn how algebraic structures are used to solve real-world problems, how number theory finds application in cryptography and other modern technologies. The book not only explains the theoretical aspects, but also offers many practical examples, which makes the material accessible and understandable. This book will be of interest not only to students of mathematical and technical specialties, but also to teachers, researchers and anyone who wants to deepen their knowledge in the field of mathematics. It is suitable for both high school students preparing for admission to the university, and for students studying in-depth courses in mathematics . If you are interested in logical problems, puzzles and want to understand how mathematics works in real life, then this publication will become a real treasure for you. The topics raised in the book cover a wide range of issues: from the basic concepts of algebra to complex theorems and their proofs. The authors pay attention to both classical aspects and modern trends, such as algorithmic number theory and its applications in digital technologies. The reader will be able to learn about key concepts such as groups, rings, fields, and how they relate to numbers and their properties. The book also addresses issues related to computational mathematics, which makes it relevant in light of modern technology. The style of the authors is distinguished by clarity and accessibility, which allows even complex mathematical concepts to be explained in simple and understandable language. They use a lot of illustrations and examples, which helps the reader to better absorb the material .. In addition, the book contains exercises that contribute to the consolidation of knowledge and the development of logical thinking .. Andrianov A. N. and Borevich Z. and . well-known mathematicians, whose works have already become classics in the field of mathematical education . Their other works, such as "