Mathematical Analysis of the Functions of Several Variables . Part 1. Differential Calculus of Functions of Several Variables: A Study by Soldatov M. A. , Round C. C. and Round E. In. is a fundamental textbook that will become an indispensable assistant for students, graduate students and teachers seeking to understand more deeply the complex aspects of mathematical analysis. This book is part of a series of tutorials designed to systematically master the theory and practice of differential calculus of functions of several variables, and is especially relevant for those who want to master the basics and prepare for more complex sections of mathematical science. The focus of this part is differential calculus, which is the cornerstone of analysis and the most important tool for solving applied problems in physics, engineering, economics and other fields. The team of authors masterfully reveals the intricacies of working with the functions of several variables, starting with the basics - definitions, limits and continuity - and gradually introduces the reader to more complex topics, such as differentials, gradients, partial derivatives and differential forms. Particular attention is paid to practical aspects, which makes the book not only a theoretical manual, but also a valuable guide for self-study and solving typical problems. The style of presentation of Soldatov, Kruglova and Kruglov is distinguished by clarity, logical consistency and attention to detail. The authors use many illustrations, real-life examples and step-by-step solutions, which facilitates the perception of even the most complex concepts. Their approach helps students not only to remember theoretical provisions, but also to learn how to apply them in practice, which is especially important in the context of a modern curriculum saturated with requirements for independent work and critical thinking. Mathematical Analysis of the Functions of Several Variables . Part 1" is ideal for students of technical, mathematical and economic specialties aged 17 to 25 years, as well as for teachers looking for high-quality educational material for their courses. It will be of interest to those who appreciate a systematic approach to learning, want to strengthen their knowledge of differential analysis and prepare for exams or writing scientific papers. In addition, the book can be an excellent guide for those who are preparing for the mathematics Olympiads and are looking for a deep understanding of the basics of analysis. The special advantage of this textbook is its structure and logical harmony .. The authors not only analyze the theoretical foundations in detail, but also offer many exercises, tasks and control questions, which contributes to the consolidation of material and the development of analytical thinking. The book raises important topics such as differential function, gradient, partial derivatives, differential forms and their application in various fields of science and technology. This makes the book not only a tutorial, but also a practical guide for those who want to learn how to apply mathematical analysis to real-world problems. A feature of the style of the authors is a combination of strict scientific accuracy with the availability of presentation. They avoid complex formulations without explanation, which makes the book understandable even for beginner students. At the same time, the material is presented in such a way that the reader gradually moves to more complex topics, without losing interest and motivation. This approach allows not only to master the theory, but also to develop the analytical skills necessary for successful study and professional activities. If you are looking for a textbook on differential calculus of functions of multiple variables that combines rigor, clarity, and practical value, "Mathematical analysis of functions of multiple variables. Part 1" under the leadership of Soldatov, Kruglova and Kruglov will be an excellent choice for you This book is the key to understanding complex mathematical concepts and their application in real life, which makes it an indispensable assistant on the way to professional growth and academic success.