"Lectures on mathematical theory of stability" is an outstanding work written by the famous Soviet mathematician and teacher Boris Nikolaevich Demidovich .. This book is an in-depth and comprehensive study of the foundations of mathematical stability theory, which is an important field in mathematics and engineering. In it, the author shares his knowledge and experience, which makes it an indispensable tool for students, graduate students and specialists working in the field of mathematical modeling, system analysis and management. From the first pages, the reader plunges into the fascinating world of mathematical concepts, where each lecture is permeated with a passion for the subject and a desire to convey complex ideas in an accessible form. Demidovich masterfully combines theory with practical examples, which allows readers not only to understand the basic principles of sustainability, but also to see their application in real-world problems. The book covers a wide range of topics, including linear and non-linear systems, methods of stability analysis, as well as various approaches to solving problems related to dynamic systems. This book will be especially interesting for those who are passionate about mathematics, physics, engineering and related sciences. Students of technical specialties, graduate students and researchers will find in it not only theoretical foundations, but also practical recommendations that will help in their scientific activities. In addition, the book can be useful to practicing engineers and analysts seeking to deepen their knowledge in the field of sustainability of systems and processes. The topics raised in the "Lectures on the mathematical theory of sustainability" are of great importance for the modern world. System sustainability is a key aspect in areas such as automation, robotics, economics and ecology. Demidovich shows how mathematical models can help predict the behavior of systems under the influence of various factors, which is especially true in a rapidly changing world. Readers will be able to see how theoretical concepts are applied to practical problems, which makes the book not only a textbook, but also a source of inspiration for future researchers. Demidovich's style is distinguished by clarity and logical presentation, which allows even complex mathematical ideas to be perceived easily and at ease. His ability to explain difficult concepts in plain language makes the book available to a wide audience. Boris Nikolayevich is also known for his other works, such as "Course of Higher Mathematics" and "Mathematical Analysis", which also deserve attention. These works, as well as "Lectures on the mathematical theory of sustainability", demonstrate his deep understanding of the subject and skill in teaching. If you are looking for a book that will help you understand the complex aspects of mathematical stability theory, “Lectures on mathematical stability theory” is what you need. It will become an indispensable assistant in your educational and professional path, opening the door to the world of mathematical analysis and system thinking. Do not miss the opportunity to immerse yourself in this fascinating and useful material that will not only enrich your knowledge, but also help you become a more competent specialist in your field.