The book "Fundamentals of the method of external forms and linear differential geometry", written by a team of authors, is a fascinating and deep immersion in the world of differential geometry, which is an integral part of modern mathematical analysis and physics. This publication will be a real discovery for students, graduate students and teachers, as well as for anyone interested in mathematics, physics and engineering. In this book, the authors offer readers a unique approach to the study of differential geometry, based on the methods of external forms. This allows not only to simplify the perception of complex concepts, but also to deepen the understanding of the relationships between different mathematical structures. The reader will be able to get acquainted with the basic concepts and theorems that underlie linear differential geometry, as well as see how these ideas are applied in various fields of science. The book will be especially interesting for those who already have basic knowledge in the field of higher mathematics and want to expand their horizons. Students of mathematical and physical faculties, graduate students and teachers will find in it a lot of useful materials that will help in preparing for classes, writing term papers and scientific papers . In addition, it will be useful to practicing engineers and physicists who want to deepen their knowledge in the field of geometry and its applications. The topics raised in the book cover a wide range of issues, ranging from the basics of linear algebra to more complex concepts such as manifolds and their properties. The authors pay special attention to the methods of external forms, which allow to solve problems related to geometry more effectively. The reader will be able to learn about how these methods are applied in relativity theory, mechanics, and other areas where geometry plays a key role. The style of the authors is distinguished by clarity and accessibility, which makes the material understandable even for those who are just beginning to get acquainted with differential geometry. The book is replete with examples and tasks that will help consolidate the knowledge gained and develop skills in solving practical problems. Each section logically follows from the previous one, creating a holistic picture of the material being studied. In addition, the team of authors includes well-known specialists in the field of mathematics, which adds additional value to the book. Their experience and knowledge make it possible to present material from different points of view, which makes reading not only informative, but also fascinating. If you are familiar with the works of authors such as Grigory Perelman or Andrei Kolmogorov, then you will be interested to see how their ideas resonate with those presented in this edition. The book "Fundamentals of the method of external forms and linear differential geometry" will become an indispensable assistant for all who seek a deep understanding of differential geometry and its applications in science and technology. If you are looking for literature that will help you not only to master the theory, but also to learn how to apply it in practice, then this publication should definitely take place on your shelf. Do not miss the opportunity to immerse yourself in the world of mathematics and discover new horizons of knowledge with this wonderful book!