The book “Lectures on private derivatives equations” by Vladimir Igorevich Arnold is not just a textbook, but a real treasure trove of knowledge for all who are interested in mathematics, physics and engineering sciences. Arnold, one of the most prominent mathematicians of the 20th century, offers readers a unique view of the world of partial-derivative equations, which play a key role in describing a multitude of phenomena in nature and technology. This book is intended for undergraduate and graduate students, as well as anyone seeking to deepen their knowledge of mathematical analysis and differential equations. If you study physics, mechanics, control theory or other related disciplines, the "Lectures on partial differential equations" will be an indispensable assistant for you. Thanks to his accessible style of presentation and deep understanding of the subject, Arnold makes complex concepts understandable even for those who are just starting their way in mathematics. In his lectures, the author not only examines the theoretical aspects of partial-derivative equations, but also illustrates their practical application. He raises important topics such as the existence and uniqueness of solutions, methods of finding them, as well as physical interpretations of the results obtained. Readers will be able to see how mathematical models help explain phenomena such as heat propagation, wave processes, and fluid dynamics. This creates an intriguing context that makes learning the material not only useful, but also fascinating. Arnold's style, known for its ability to explain complex things in simple language, makes this book especially attractive. He masterfully combines strict mathematical formulation with intuitive understanding, which allows readers not only to absorb material, but also to develop their own thinking. Arnold is also known for his work in topology and differential geometry, and his approach to partial differential equations is permeated by the same principles of clarity and logic. The book "Lectures on partial differential equations" also touches on the philosophical aspects of mathematics, emphasizing that mathematics is not just a set of formulas and algorithms, but a way of understanding the world around us. Arnold inspires readers to reflect on how mathematics can help solve real-world problems, and how it relates to other sciences. This work will be an excellent addition to the library of any student or professional seeking to deepen their knowledge of mathematics and its applications. If you are looking for books on mathematical analysis, differential equations or physics, "Lectures on partial differential equations" should definitely be on your list. Readers interested in works such as "Methods of Mathematical Physics" P. G. Grigorieva