The book "Differential calculus (theory and applications)" by B. M. Tikhomirov is a fascinating and deep dive into the world of mathematical analysis, which will become an indispensable tool for students, teachers and anyone interested in mathematics at a deeper level. In this work, the author not only outlines the theoretical foundations of differential calculus, but also offers many practical applications, which makes it especially valuable for those who want to see how abstract mathematical concepts are applied in real life. The book covers a wide range of topics, ranging from the basic concepts of derivative to more complex topics such as mean-value theorems and applications of differential calculus in various fields of science and technology. Tikhomirov masterfully explains complex ideas, making them understandable, which is especially important for students who are just starting their way in mathematics. His style of presentation is clear and logical, which allows the reader not only to absorb the material, but also to develop critical thinking. For whom is this book intended? First of all, it will be useful to students of mathematical and engineering specialties, as well as to everyone who studies physics, economics and other sciences, where understanding of mathematical foundations is required. However, not only students will find valuable information in it - the book will also be interesting to teachers who will be able to use it as a guide and methodological guide for their classes. It can also attract the attention of mathematics lovers who want to deepen their knowledge and understand how differential calculus affects various aspects of our lives. The topics that are raised in the book cover not only theoretical aspects, but also practical applications. For example, the author considers how derivatives are used to find the extremes of functions, which is a key point in optimizing processes in economics and engineering. In addition, Tikhomirov pays attention to the graphical representation of functions and their derivatives, which helps the reader to better understand how to visualize mathematical concepts. This makes the book especially valuable for those who prefer to see rather than just read about mathematical ideas. Style B. M. Tikhomirov can be described as accessible and at the same time deep. He is able to find a balance between theory and practice, which makes his work attractive to a wide audience. In his arsenal there are other well-known works, such as "Integral calculus" and "Mathematical analysis", which also deserve attention and can complement the knowledge gained from "Differential calculus" .. Differential calculus (theory and applications) is not just a textbook, but a whole world in which the reader can immerse himself to understand how mathematics shapes our perception of the world around him. It will become a reliable companion on the way to mastering one of the most important areas of mathematics, opening up new horizons and opportunities for the reader. If you are looking for a quality tutorial that will help you not only learn differential calculus, but also learn how to apply it in various fields, then this book is exactly what you need.