The book "Geometric methods in the theory of ordinary differential equations" by Vladimir Igorevich Arnold is an outstanding work that opens the world of mathematical analysis and geometry to the reader, connecting them into a single harmonious system. Arnold, known for his in-depth research in mathematics, offers a unique approach to the study of ordinary differential equations that will be of interest to both students and professional mathematicians. In this work, the author immerses the reader in the world of differential equations, considering them not only as abstract mathematical constructs, but also as living objects with their geometry and dynamics. Arnold uses geometric methods to analyze the solutions of equations, which allows us to see their behavior in space and time. He emphasizes the importance of visualizing mathematical processes, which makes the material more accessible and understandable. The reader will be able to learn how graphical representation can help in solving complex problems and in understanding the nature of mathematical models. The book will be of particular interest to senior students of mathematical and physical faculties, as well as graduate students and researchers engaged in the theory of differential equations. If you are interested in mathematics, physics, engineering or even economics, where differential equations play a key role in modeling processes, then this work will become an indispensable source of knowledge and inspiration for you. 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 aspects, such as the stability of solutions and their qualitative analysis. Arnold not only explains the theoretical foundations, but also illustrates them with real-life examples, which makes the material more alive and relevant. It shows how geometric methods can be applied to practical problems, which is especially important in the modern world, where mathematics finds application in a wide variety of fields. Arnold's style is clear and logical, which allows the reader to easily follow his thoughts and ideas. His approach to teaching mathematics has always been focused on understanding rather than memorizing formulas. This makes his books not only tutorials, but also real guides to the world of mathematics. Among Arnold's other notable works are Ordinary Differential Equations and Geometry and Topology, which have also been recognized for their depth and accessibility. If you are looking for a book that will help you to better understand ordinary differential equations and their geometric aspects, "Geometric methods in the theory of ordinary differential equations" will be an excellent choice. This work will not only expand your knowledge, but also inspire new research and discoveries in the field of mathematics. Read, explore and discover an amazing world where geometry and analysis are intertwined in a single dance of numbers and shapes.