The book “Lectures on the theory of ordinary differential equations” by Vladimir Igorevich Arnold is not just a textbook, but a real treasure trove of knowledge for everyone who wants to understand the world of mathematics and its applications more deeply. Arnold, a well-known Russian mathematician, left a bright mark in various fields of science, and in this book he shares his unique views on the theory of ordinary differential equations, which makes it mandatory for students and professionals alike. The book focuses on ordinary differential equations, which are the main tool for describing dynamical systems in a variety of fields, from physics and engineering to biology and economics. Arnold does not just expound theory, he immerses the reader in the world of mathematical concepts, focusing on intuitive understanding and visualization. His style of presentation is clear and logical, which allows even complex ideas to be perceived easily and with interest. The book will be especially useful for students of mathematical, physical and engineering specialties, as well as graduate students and teachers who are looking for an in-depth understanding of the topic. However, its value is not limited only to the academic circle - it can also attract the attention of mathematics lovers seeking to expand their horizons and learn more about the application of differential equations in real life. If you are interested in topics such as system dynamics, mathematical modeling or even the philosophy of science, this book will be a real discovery for you. Arnold raises many important topics such as the existence and uniqueness of solutions, sustainability, and qualitative analysis of dynamical systems. It also considers various methods of solving differential equations, including numerical approaches, which makes the material relevant and practical. The reader will be able not only to get acquainted with the theoretical foundations, but also to see how this knowledge is applied in practice, which is especially important in the modern world, where mathematics plays a key role in scientific and technical achievements. Arnold's style differs from the traditional approach to teaching mathematics. It uses many examples and illustrations, which makes the material more accessible and understandable. His ability to explain complex concepts in simple language and with the help of illustrative examples allows the reader not only to remember the material, but also to understand its essence. This makes "Lectures on the theory of ordinary differential equations" not just a textbook, but a real guide to the world of mathematics. If you are already familiar with Arnold's other works, such as Geometry and Topology or Ordinary Differential Equations, you will surely appreciate his unique approach and deep understanding of the subject. This book will be a logical continuation of your study and will help you expand your knowledge in the field of differential equations. In conclusion, "Lectures on the Theory of Ordinary Differential Equations" is not just a book, but a whole era in the study of mathematics. It inspires, makes you think and opens up new horizons for everyone who is ready to plunge into the fascinating world of differential equations. If you are looking for a high-quality, deep and accessible presentation of the topic, this book will become your reliable companion in the mathematical journey.