"Geometric methods in the theory of ordinary differential equations" is an outstanding work of Vladimir Igorevich Arnold, one of the most famous mathematicians of our time. This book is not just a textbook, but a real treasure trove of knowledge, in which the author shares his unique vision and deep understanding of complex mathematical concepts. The book focuses on ordinary differential equations, which play a key role in mathematics and its applications. Arnold explores the geometric aspects of these equations, showing how visualization and geometric methods can greatly simplify their analysis and solution. He introduces the reader to a world where mathematics becomes not only an abstract science, but also an art, where each equation can be represented as a geometric figure, and each solution as a point on a plane. The book will be of interest not only to professional mathematicians, but also to students, graduate students and anyone who seeks to deepen their knowledge in the field of differential equations. It is suitable for those who are interested in mathematics, physics, engineering and even economics, since ordinary differential equations are widely used in various fields of science and technology. Readers interested in mathematical theory and practical problems will find in this book many useful ideas and methods that can be applied in their research and projects. The topics raised in the book cover a wide range of issues, ranging from the foundations of the theory of ordinary differential equations to more complex concepts such as the stability of solutions and their geometric interpretation. Arnold masterfully combines theory with practice, which makes his work especially valuable for those who want not only to understand, but also to apply the knowledge gained. He emphasizes the importance of an intuitive understanding of mathematical concepts, which allows readers not only to memorize formulas, but also to be aware of their essence. Arnold's style is clear and accessible, making his books easy to read, even when it comes to complex topics. His ability to explain difficult things in simple language makes "Geometric methods in the theory of ordinary differential equations" an ideal choice for those who are just starting their way in the world of mathematics, as well as for experienced professionals who want to refresh their knowledge. In addition, Vladimir Igorevich Arnold is the author of many other famous works, such as