The book “Geometric Methods in the Theory of Ordinary Differential Equations” by Vladimir Igorevich Arnold is an outstanding work that immerses the reader in the world of mathematical analysis and geometry, revealing complex concepts with amazing clarity and depth. Arnold, known for his significant contributions to mathematics, not only demonstrates his knowledge, but also shares a unique vision that can be useful to both students and professional mathematicians. In this book, the author explores ordinary differential equations (ODEs) from the point of view of geometry, which allows us to see them not just as abstract mathematical constructs, but as objects that have their own geometric nature. Arnold offers readers unique methods and approaches that help to visualize and understand the dynamics of the systems described by the ODU. This makes the book especially valuable for those who seek not only to solve equations, but also to understand their behavior and structure. The book will be of interest to a wide range of readers: from senior students of mathematical faculties to graduate students and researchers working in the field of mathematical modeling and theory of dynamic systems. If you are passionate about mathematics, physics or engineering and want to deepen your knowledge in the field of differential equations, this work will be a real find for you. Arnold writes in an accessible and understandable way, which makes his work suitable even for those who are just beginning to get acquainted with this topic. The topics raised in the book cover a wide range of issues, ranging from basic concepts to complex theoretical aspects. Arnold focuses on the importance of the geometric approach, which allows not only to find solutions to equations, but also to analyze their properties. It discusses key concepts such as sustainability, phase portraits, and system dynamics, making the material relevant to contemporary research in mathematics and related fields. Arnold's style is clear and logical, which allows the reader to easily follow his thoughts. It uses many examples and illustrations, which contributes to a better understanding of complex ideas. In addition, the author is not afraid to introduce the reader to the world of more abstract concepts, which makes his book not only a textbook, but also a source of inspiration for further research. If you are interested in such works as "Differential equations and dynamical systems" or "