The book *Methods of Solving Ordinary Differential Equations* by N.M. Matveev is a comprehensive and insightful work that will become an invaluable resource for students, graduate researchers, and professionals in mathematics and engineering. In this volume, the author shares his expertise and experience, offering readers not only the theoretical foundations but also practical techniques for solving ordinary differential equations (ODEs), which underpin many scientific and applied disciplines. From the very first pages, Matveev immerses the reader in the world of differential equations, explaining their significance and widespread applications across fields such as physics, mechanics, biology, and economics. He begins with simple examples, gradually introducing more complex methods of integration and demonstrating how ODEs help model real-world processes like motion, temperature changes, and population dynamics. This approach makes the book especially valuable for those who want to understand both the theory and its practical use. Ideal for advanced students in mathematics and engineering, as well as seasoned researchers seeking new methods for tackling practical problems, this book is a true find for anyone passionate about mathematics, physics, or engineering and eager to deepen their knowledge of differential equations. A key focus of the book is the classification of ordinary differential equations and the methods used to solve them, including separation of variables, integrating factors, and the method of characteristics. Matveev not only explains how to apply these techniques but also provides numerous examples to reinforce understanding. He also pays attention to numerical methods, making the book highly relevant for modern readers working with computer models. The author's clear and accessible style makes even the most complex concepts easy to grasp. N.M. Matveev is renowned for his scientific works and textbooks, which have earned recognition both in Russia and internationally. His writings are characterized by a deep understanding of the subject and an ability to explain intricate ideas in simple language, making his books not only useful but also engaging to read. *Methods of Solving Ordinary Differential Equations* will serve as an excellent addition to the library of anyone interested in mathematics and its applications. It can be used both as a textbook and as a reference guide for practicing professionals. Those seeking information on how to solve differential equations might search for terms like “methods for solving ODEs,” “differential equation integration,” or “differential equations textbook.” In conclusion, N.M. Matveev’s book is more than just a textbook — it’s a true guide to the world of ordinary differential equations. It inspires further study of mathematics and opens new horizons for those ready to explore this fascinating and vital field of science. If you wish to expand your skills and knowledge in solving differential equations, this volume will be your reliable companion on that journey.