The method of vector functions of Lyapunov in the theory of stability, written by Abdullin R. Z. , Sailors V. M. and other authors, is a unique study in the field of mathematical theory of stability of dynamical systems. This work will become an indispensable assistant for students, graduate students and specialists in mathematics, physics, engineering and related sciences. The book focuses on the Lyapunov vector function method, which is a powerful tool for analyzing the stability of systems. The authors consider in detail the basic principles and approaches that allow us to assess the stability of various dynamic processes .. The book not only explains the theoretical aspects of the method, but also offers practical examples of its application, which makes the material accessible and understandable to readers with different levels of training. Who can like this book? First of all, it will be of interest to students and graduate students studying sustainability theory and dynamic systems. Engineers and researchers working in the field of automation, robotics and control systems will also find in it many useful ideas and solutions. In addition, the book can attract the attention of teachers who want to deepen their knowledge in the field of mathematical analysis and stability theory .. The topics raised in the book cover a wide range of issues related to the sustainability of systems. The authors discuss both linear and nonlinear systems, and also consider various types of sustainability, including asymptotic and global. Particular attention is paid to methods for constructing Lyapunov vector functions and their properties, which allows the reader to understand more deeply how these methods can be used to solve practical problems. The style of the authors is clear and structured, which allows the reader to easily assimilate complex mathematical concepts. They use a lot of illustrations and graphics, which makes the material more visual and accessible. In addition, the book contains tasks and exercises that will help to consolidate the studied material and develop the skills of applying the Lyapunov vector functions method in practice. Authors, P. Z. Abdullin and B. M. Sailors, known for their scientific work in the field of stability theory and dynamical systems Their previous publications have also received recognition in the scientific community, which confirms the high level of their expertise and professionalism. This book is a logical continuation of their research and represents an important contribution to the development of sustainability theory. The book "Method of vector functions of Lyapunov in the theory of stability" not only enriches the reader with new knowledge, but also inspires further research in this field. It will become a reliable guide for those who seek to understand complex mathematical concepts and apply them in practice. If you are looking for a qualitative and in-depth study in the field of stability of dynamic systems, this work should definitely take place on your shelf. Do not miss the opportunity to immerse yourself in the world of mathematical research and discover new horizons in sustainability theory with this book.