The book "Convex analysis and its applications" by the authors Magaril-Ilyaev G. G. and Tikhomirov V. M. is a fascinating and in-depth study in mathematics that will be of interest to both students and professional mathematicians. This work not only introduces the reader to the basics of convex analysis, but also demonstrates its practical application in various fields of science and technology. Convex analysis is a branch of mathematics that studies the properties of convex sets and functions. This topic may seem highly specialized at first glance, but it covers a wide range of issues, from optimization to game theory and economic models. The authors, possessing rich experience and deep knowledge, offer the reader not only theoretical calculations, but also practical examples that make the material accessible and understandable. The book will be of interest to senior students of mathematical and engineering specialties, as well as graduate students and teachers who want to deepen their knowledge in this area. It will also attract the attention of researchers working in related disciplines such as economics, physics, and computer science. If you are passionate about mathematics and want to understand how theoretical concepts can be applied in practice, this work will be a real find for you. The topics raised in the book cover a wide range of issues, including the properties of convex sets, optimization techniques, and the application of convex analysis in various scientific studies. The authors focus on how convex analysis can be used to solve real-world problems, making the book particularly valuable for those seeking practical applications of mathematical knowledge. The style of writing Magaril-Ilyaev and Tikhomirov is clear and logical . They are able to explain complex concepts in a simple and accessible language, which allows the reader to easily digest the material. In addition, the book contains many illustrations and examples that help to consolidate the knowledge gained .. This makes reading not only useful, but also fascinating. “Convex analysis and its applications” is not just a textbook, but a real encyclopedia of knowledge, which can become a desktop book for anyone interested in mathematics. The authors are also known for their other work in mathematics, and their experience and authority in the field add value to this book. Readers who are already familiar with other works of these authors will find in this book the continuation of their research and new horizons for study. If you are looking for literature that will help you deepen your knowledge of mathematics, as well as learn how to put theory into practice, Convex Analysis and its Applications will be an excellent choice. This book will not only expand your horizons, but also help you become more confident in your mathematical skills. Do not miss the opportunity to get acquainted with this wonderful work, which can change your perception of mathematics and its application in the real world.