The book "Differential Equations: A Study Manual", created by the team of authors, is an indispensable source of knowledge for students, teachers and specialists seeking a deeper understanding of one of the key disciplines of mathematical analysis. This edition is not just a textbook - it is a guide to the complex but fascinating world of differential equations, revealing their theoretical foundations and practical application. The focus of this book is the variety of methods for solving differential equations, ranging from classical integration methods to modern approaches, such as numerical methods and analytical techniques. The authors masterfully combine theory and practice, showing how differential equations are used in modeling physical processes, biological systems, engineering problems, and economic models. The reader will find here not only strict formulas and proofs, but also real examples illustrating how these equations help to understand and predict the behavior of complex systems. This book is ideal for students of technical, mathematical and natural sciences faculties, as well as graduate students and teachers looking for reliable educational material for in-depth study of the subject . It will also be useful for those who have already encountered differential equations, but want to systematize knowledge or expand their skills in solving non-standard problems. Adult specialists working in the field of engineering, economics or information technology will find here practical recommendations and modern methods that can be applied in professional activities. The peculiarity of this manual is its clarity and structure. The authors use an accessible language, avoiding unnecessary complex terminology, which makes the material understandable even for those who are just beginning to get acquainted with differential equations. At the same time, the book is not inferior in depth and academic rigor, which allows it to be used as a teaching tool for preparing for exams, PhD and doctoral dissertations . The style of presentation combines the rigor of scientific explanations and the liveliness of the presentation, which makes reading not only useful, but also fascinating. Particular attention is paid to modern aspects of solving differential equations, including numerical methods, computer modeling and the use of software. This makes the book relevant for those who want to keep up with progress and apply the knowledge gained in real-world tasks. The authors also consider the historical aspects of the development of the theory of differential equations, which helps to understand how this area of mathematics has evolved and what challenges scientists faced on the way to modern achievements. If you are looking for a book that not only systematizes knowledge, but also inspires further study, “Differential Equations: A Study Guide” will be an excellent choice for you. This edition is not just a collection of formulas, but a real guide to the world of mathematical models, revealing their secrets and showing how mathematics helps to understand the world around us. Get inspired, explore and expand your horizons along with this unique guide, which deservedly occupies a place in the library of everyone who appreciates the accuracy, logic and beauty of mathematical thinking.