The book “The principle of maximum in optimal management” by Lev Pontryagin is an outstanding work that has become fundamental in the field of control theory and optimization. Pontryagin, a well-known Soviet mathematician and Stalin Prize winner, offers readers a unique perspective on the methods of optimal control of dynamical systems. This work not only enriches the theoretical base, but also opens up new horizons for practical application in various fields, such as economics, engineering and even biology. The book immerses the reader in the world of mathematical models and optimization problems, offering an in-depth understanding of the principles underlying effective management. Pontryagin introduces the reader to the concept of maximum, which allows finding optimal solutions in conditions of uncertainty and dynamics. It looks at various scenarios and problems where decisions need to be made based on changing conditions, and shows how one can achieve the best result using mathematical methods. This book will be of interest not only to specialists in mathematics and engineering, but also to anyone who seeks to understand how to make optimal decisions in their lives or professional activities. Students, graduate students, researchers and practitioners will find in it many useful ideas and approaches that can be applied in real-life situations. In addition, the book will be useful to managers and entrepreneurs who want to optimize their business processes and improve the efficiency of their teams. The topics raised in the book cover a wide range of issues related to optimization and management. Pontryagin explores how mathematical methods can be used to analyze complex systems, identify patterns, and find optimal solutions. It also looks at the impact of external factors on decision-making and suggests approaches to minimizing risks. These aspects make the book relevant for modern readers seeking effective management in a rapidly changing world. Pontryagin's style is distinguished by clarity and logical presentation, which allows even complex mathematical concepts to be perceived easily and with interest. His approach to explaining theoretical fundamentals and practical applications makes the book available to a wide audience. Lev Semenovich is also known for his other works, such as "Mathematical Theory of Management", which also deserve attention and can complement the understanding of the topics raised in the "Principle of Maximum". If you are looking for a book that will help you understand the intricacies of optimal management and teach you how to make informed decisions, the “Principle of maximum in optimal management” will be an excellent choice. This work will not only enrich your knowledge, but also inspire new ideas and approaches in your professional activities. Do not miss the opportunity to immerse yourself in the world of mathematical analysis and optimization, which will open up new horizons and opportunities for you.