The Differential Equations . Textbook" by Samoilenko A. M. , Curved C. A. and Perestyuk N. A. is an indispensable resource for students and teachers studying one of the most important and challenging areas of mathematics Differential equations are not just a set of formulas and theorems, they are the key to understanding the many processes occurring in nature and technology. In this manual, the authors offer readers a deep immersion in the world of differential equations, their classification, methods of solution and practical application. The book covers a wide range of topics, ranging from the foundations of theory to more complex concepts, such as systems of differential equations and their applications in various fields of science and engineering. The authors use an accessible and understandable language, which makes the material available to students studying mathematics in the first courses of universities, as well as for those who want to refresh their knowledge in this area. If you are looking for a tutorial that will help you not only to master the theory, but also to learn how to apply it in practice, then this publication will become your reliable companion. The book will be of interest not only to students of mathematical and engineering specialties, but also to anyone who wants to understand how mathematical models describe real processes. For example, biologists can find useful methods for modeling populations here, and physicists can find useful methods for describing the dynamics of moving bodies. This manual will also be useful to graduate students and teachers who are looking for quality materials for the preparation of lectures and seminars . One of the features of this tutorial is its structure. Each chapter begins with a theoretical introduction, followed by examples and tasks of varying complexity. This allows the reader to gradually master the material and consolidate knowledge in practice. The authors pay attention not only to the methods of solution, but also to the analysis of the results obtained, which is an important part of mathematical education. The topics raised in the book cover both classical and modern approaches to the study of differential equations. Readers will be able to familiarize themselves with the methods of separating variables, integrating factors, as well as with more complex concepts, such as numerical methods and qualitative analysis. This makes it a universal tool for studying both theoretical and practical aspects of differential equations. The style of the authors is distinguished by clarity and logical presentation, which makes complex topics more accessible for understanding. Samoilenko A . M. and its co-authors are known for their scientific works and teaching aids, which have already won recognition in the academic environment. Their experience and deep knowledge in the field of mathematics allow us to create high-quality and relevant material that will be useful both for self-study and for use in the educational process. If you are looking for a book that will help you understand differential equations and their application, "Differential Equations. Training manual" will be an excellent choice. This edition will not only enrich your knowledge, but also inspire you to further study mathematics and its practical application in various fields. Do not miss the opportunity to take a step towards understanding the complex but fascinating world of differential equations!