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 beauty and depth to the reader. Arnold, known for his outstanding achievements in the field of mathematics, in this work offers a unique look at ordinary differential equations (ODEs), using geometric methods as the main tool of analysis. In this book, the author not only outlines the theoretical aspects of OCA, but also demonstrates how geometric approaches can greatly facilitate understanding and solving complex problems. Arnold masterfully combines abstract mathematical concepts with intuitive visual images, which makes the material accessible and understandable even to those who are not professional mathematicians. The reader is immersed in a world of curves, trajectories and phase spaces, where each equation has its own geometric interpretation. The book will be of interest to students studying mathematics and physics, as well as teachers who are looking for new approaches to learning. It will also attract the attention of researchers and practitioners working in applied mathematics, mechanics, and engineering. The age category of readers can range from high school students to graduate students and professionals seeking to deepen their knowledge in ODU theory. The topics that Arnold raises cover a wide range: from the basics of differential equations to their application in various scientific fields. He discusses concepts such as the sustainability of solutions, bifurcations and integrability of systems, which allows the reader not only to master the theory, but also to see the practical application of this knowledge. The book also touches on the philosophical aspects of mathematics, emphasizing the beauty and harmony that can be found in numbers and equations. Arnold's style is distinguished by clarity and logical presentation, which makes his work especially valuable for readers. He skillfully uses examples and illustrations to illustrate complex ideas, making them more accessible. His other well-known works, such as Methods of Mathematical Physics and Geometry and Dynamics, also demonstrate his ability to connect theory with practice, making him one of the most respected authors in the field of mathematics. The book "Geometric methods in the theory of ordinary differential equations" is not just a textbook, but also a real source of inspiration for those who want to deepen their knowledge in mathematics. It opens up new horizons for exploration and understanding, allowing readers to see the world of OCA from an entirely new perspective. If you are looking for literature that combines the theory, practice and philosophy of mathematics, this work will be a real find for you. Do not miss the opportunity to touch the mathematical magic that Arnold offers This book will be your reliable companion in the study of ordinary differential equations and geometric methods, opening up new horizons of knowledge and understanding.