The book "Convex Analysis: Theory and Applications" by Magaril-Ilyaev G. G. and Tikhomirov V. M. It is an in-depth and comprehensive study of one of the key areas of mathematics that finds application in a wide variety of fields, from economics to engineering. This edition will be a real find for students, graduate students, teachers and anyone interested in modern mathematical methods and their practical applications. Convex analysis is not just a theory, it is a whole world in which geometry, linear algebra and optimization are intertwined. The authors, with rich experience and in-depth knowledge in this area, offer the reader not only theoretical foundations, but also practical examples that help to better understand complex concepts. The book covers a wide range of topics, ranging from the basics of convex sets to more complex issues related to convex functions and their application in various optimization problems. One of the features of this publication is its accessibility to a wide audience. The authors try to explain complex mathematical concepts in a simple and understandable language, which makes the book ideal for students who are just beginning to study this area, as well as for practitioners who want to refresh their knowledge. If you study at the Faculty of Mathematics, Physics, Economics or Engineering, then this book will become an indispensable assistant in your educational process. The topics raised in Convex Analysis cover not only theoretical aspects, but also practical applications. The book demonstrates how convex analysis is used in real-world problems such as resource optimization, data analysis, and even in the development of algorithms for machine learning. This makes it particularly relevant in today's world, where mathematical methods are becoming increasingly important in various industries. The style of the authors is distinguished by the clarity and logic of the presentation . They not only share their knowledge, but also inspire the reader to further explore the topic. Magaryl-Ilyaev and Tikhomirov are known for their work in mathematics and applied sciences, and their experience allows them to delve deeply into the material, making it accessible and interesting. Their previous work was also popular among students and professionals, which confirms the high level of their expertise. The book "Convex Analysis: Theory and Applications" will be of interest not only to those who study mathematics, but also to those who work in the field of applied sciences, such as economics, engineering and computer science. If you are looking for literature that will help you understand how to apply mathematical methods in real life, this book will be your reliable guide. In conclusion, Convex Analysis: Theory and Applications is not just a textbook, but a real encyclopedia of knowledge that will help you immerse yourself in the world of convex analysis and its applications. This edition will be your faithful companion in the study of mathematics and will open new horizons in understanding complex concepts. Do not miss the opportunity to touch this fascinating world, which can change your idea of mathematics and its role in modern society.