The Theory of Extreme Tasks by A. D. Ioffe and B. M. Tikhomirov is a fascinating and in-depth study that immerses the reader in the world of mathematical analysis and optimization. This work will be a real find for anyone interested in mathematics, physics, engineering and related sciences. The authors, possessing rich experience and deep knowledge in the field of optimization theory, offer the reader a unique view on solving problems that require finding extremes highs and lows. The book covers a wide range of topics, ranging from basic concepts to more complex concepts such as Lagrange methods, convex functions, and multidimensional optimization problems. Each section is imbued with logic and rigor, which makes the material understandable even if you are not a professional mathematician. However, despite its scientific orientation, the text is written in a lively and understandable language, which allows the reader not only to assimilate information, but also to enjoy the reading process. "Extreme problem theory" will be of interest to both students and teachers, as well as to everyone who works in the field of applied mathematics. If you are fond of solving complex problems, like to understand the intricacies of mathematical models or just want to expand your knowledge in this area, then this book will be a real guide for you. It will also be useful to specialists working in the field of economics, statistics and management, where optimization skills play a key role. The topics raised in the book concern not only theoretical aspects, but also practical applications. The authors show how mathematical models can be used to solve real problems, which makes the material especially relevant in the modern world, where process optimization becomes a necessity. The reader will be able to see how theoretical knowledge is applied in practice, which inspires further research and experiments. The style of the authors is clear and logical, which makes it easy to follow their thoughts. A. D. Ioffe and B. M. Tikhomirov is known for his scientific works and research in the field of mathematical analysis and optimization, and in this book they present their ideas in an accessible and fascinating form. Their other works are also noteworthy, and Extreme Task Theory could be a great start to getting to know their scientific heritage. If you are looking for books in mathematics that will help you deepen your knowledge in the field of optimization, then “Extreme Problem Theory” will be the ideal choice for you. It can be useful not only for undergraduate and graduate students, but also for professionals seeking to improve their skills in solving complex problems. Readers interested in works such as "Optimization" J. B. Castello or "