The book "Variation calculus and optimal management (compendium of the course of lectures)" by B. M. Tikhomirov is a deep dive into the world of mathematical analysis, where theory meets practice. This publication is not just a summary of lectures, but a whole training course that allows the reader to master the complex concepts of variational calculus and optimal control applied in various fields of science and technology. Variational calculus is a branch of mathematics that studies the extreme values of functionals, and optimal control is a discipline that searches for optimal strategies for managing dynamical systems. In Tikhomirov's book, these two directions are combined, creating a powerful tool for solving real problems arising in engineering, economics and other applied sciences. The reader will be able to learn how mathematical methods can not only describe, but also optimize processes, which makes the material especially relevant in the modern world, where efficiency and rationality play a key role. The book will be of interest to students and graduate students of technical and mathematical specialties, as well as specialists working in the field of applied mathematics, economics, physics and engineering .. It is suitable for those who seek to deepen their knowledge in mathematics and are looking for practical applications of theoretical concepts. Thanks to the available language of presentation and a clear structure, even those who are just beginning to get acquainted with the calculus of variation, will be able to find useful and understandable explanations in it. The topics raised in the book cover a wide range of issues, from the basics of calculus to the more complex aspects of optimal control. The author examines in detail the methods of solving problems, including the methods of Lagrange and Hamilton, as well as various approaches to optimization. An important part of the book is the analysis of examples, which allows the reader not only to understand the theory, but also to see its application in practice. This makes the learning process more exciting and meaningful. Style B. M. Tikhomirov is distinguished by clarity and logic .. He skillfully combines theoretical calculations with practical examples, which allows the reader to easily assimilate the material. The author is also known for his other work in mathematics and mechanics, which confirms his in-depth knowledge and experience in this field. His approach to learning has always been focused on creating a solid foundation for further study, making his books valuable to students and practitioners.[citation needed] “Variation calculus and optimal management” is not just a textbook, but a real find for those who want to master modern mathematical methods and apply them in their professional activities. This book will be an indispensable assistant in preparing for exams, writing term papers and diploma papers, as well as in scientific research. If you are looking for literature that will help you understand complex mathematical concepts and teach you how to apply them in practice, then this book should definitely take a worthy place on your shelf. Immerse yourself in the world of variational calculus and optimal control with B. M. Tikhomirov and discover new horizons in mathematics and its application!