Algebraic Groups and Number Theory by A. Platonov and B. Rapinchuk is a fascinating and in-depth study that opens up to the reader the world of algebraic structures and their connection with the theory of numbers. This work will be a real find for students, graduate students and anyone interested in modern areas in mathematics. If you are looking for literature that will not only expand your knowledge, but also inspire new research, then this book is exactly what you need. The authors focus on algebraic groups, powerful tools that play a key role in various areas of mathematics, including number theory, geometry, and even physics. Platonov and Rapinchuk masterfully explain complex concepts, making them available to a wide audience. The book begins with the basics, gradually deepening into more complex topics, which allows the reader not only to learn the material, but also to see how algebraic groups interact with other mathematical structures. One of the main themes of the book is the relationship between algebraic groups and solutions of diophantine equations. The authors show how these groups can be used to find whole solutions to equations, which is one of the central problems in number theory. Readers will be able to see how algebraic groups help in understanding concepts such as modular forms and their relationship to numbers, which makes the book relevant and interesting for anyone who wants to deepen their knowledge in this area. The book will be especially useful for those studying mathematics at the master's or postgraduate level, as well as teachers and researchers working in the field of algebra and number theory. It is suitable for those who are just starting their way in mathematics, and for experienced professionals who want to update their knowledge or find new ideas for research. Through accessible language and clear explanations, even complex concepts become comprehensible and fascinating. The style of Platonov and Rapinchuk is clear and logical, which allows the reader to easily follow the course of thought of the authors. They use many examples and tasks that help to consolidate theoretical material and develop analytical thinking. This book is not only educational, but also inspires further research, encouraging the reader to ask questions and seek answers. "Algebraic groups and number theory" is not just a textbook, but a real encyclopedia of knowledge that covers a wide range of topics and problems. It raises important questions about the nature of numbers and algebraic structures, making it relevant to modern research. If you are interested in how algebraic groups can change our understanding of numbers, then this book will be your reliable companion in this fascinating journey. Do not miss the opportunity to immerse yourself in the world of algebraic groups and number theory, discovering new horizons of mathematics. The book of Platonov and Rapinchuk is your key to understanding complex mathematical concepts and their application in real life. Read, explore and be inspired by new ideas that will help you in your scientific and educational endeavors.