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 theory, where geometry and analysis are intertwined in amazing harmony. Arnold, one of the most famous mathematicians of the 20th century, offers a unique look at ordinary differential equations, using geometric approaches to investigate and solve them. In this book, the author does not just describe methods and theories, but creates a holistic picture in which each concept logically follows from the previous one. Arnold masterfully combines rigorous mathematical proofs with intuitive geometric illustrations, making the material accessible and understandable even to those who are not professional mathematicians. The reader is waiting for a fascinating journey through various aspects of differential equations, where each new discovery causes a desire to delve deeper into the study. The book will be of particular interest to undergraduate and graduate students studying mathematics, physics and engineering sciences. It will also attract the attention of teachers and researchers who are looking for new approaches to teaching and research in the field of differential equations. If you are passionate about mathematics and want to see how geometry can be used to solve complex problems, this book will be a real find 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 concepts, such as the stability of solutions and their geometric interpretation. Arnold not only explains how to apply geometric methods, but also shows why they work, which makes his work especially valuable for a deep understanding of the subject. Arnold's style is clear and logical. He is able to explain complex ideas in simple language, which makes his books available to a wide audience. In the "Geometric methods" the reader will find many examples, illustrations and tasks that will help to consolidate the knowledge gained. This work is not only a textbook, but also an inspiring guide for those who want to expand their horizons in mathematics. If you are familiar with Arnold's other works, such as Ordinary Differential Equations or Geometry and Dynamics, then you already know what level of depth and quality can be expected from this author. His ability to connect theory with practice makes each of his books a real treasure for readers seeking understanding and exploration. The book “Geometric Methods in the Theory of Ordinary Differential Equations” is not just a textbook, but a real encyclopedia of ideas that inspires further research and discoveries. She will become an indispensable assistant for anyone who wants not only to learn, but also to love mathematics, to see in it beauty and harmony. If you are looking for literature that will help you deepen your knowledge of differential equations and open new horizons in your mathematical journey, this book is exactly what you need.