The book “Course of Differential Geometry (2001-2002)”, created by the team of authors, is a unique educational resource that immerses the reader in the exciting world of modern mathematics. This book is not just a collection of theoretical calculations, but a real guide to the complex but incredibly beautiful concepts of differential geometry, revealing to the reader the secrets of curves, surfaces and varieties that underlie many modern scientific and engineering disciplines. What makes the "Differential Geometry Course (2001-2002)" especially attractive to a wide range of readers? First of all, it is designed for undergraduate and graduate students, as well as for teachers and researchers looking for a deep and systematic presentation of the topic. However, thanks to the clarity of the presentation and the wealth of examples, the book will be interesting to those who are just beginning to get acquainted with differential geometry, as well as lovers of mathematics who want to expand their horizons. This book is an ideal choice for those who appreciate not only a strict approach, but also the creative perception of complex concepts. The author's team, known for its professionalism and pedagogical skills, created a work that combines theoretical rigor and practical applicability. The book deals in detail with such important topics as the theory of curves and surfaces, the theory of manifolds, metric structures, geodetic lines and parallel transport. Particular attention is paid to the visualization of complex concepts, which makes the material more accessible and understandable. The presentation style is distinguished by clarity and logical consistency, which allows the reader not only to assimilate the material, but also to feel the beauty and harmony of differential geometry. This book is noteworthy not only because it is a fundamental textbook, but also because it raises topical issues related to modern applications of geometry in physics, computer graphics, robotics, and relativity theory. It reveals the connections between abstract mathematical structures and real-world problems, making it a valuable tool for those who want to understand how mathematics helps to model and analyze the world around them. A special place in the book is occupied by the style of the author, which is distinguished not only by academic rigor, but also by a lively, fascinating approach to the presentation of the material. The team of authors uses vivid illustrations, understandable schemes and examples from real life, which contributes to a deeper perception of complex concepts. As a result, even the most difficult topics turn into interesting stories about curved lines, surfaces and varieties that seem almost alive and very close. If you are already familiar with classical mathematics and are looking for a modern, comprehensive and inspiring introduction to differential geometry, the “Differential Geometry Course (2001-2002)” will be an indispensable assistant for you. This book is not just a textbook, but a real source of inspiration, revealing the beauty and depth of one of the most elegant branches of mathematics. It is ideal for those who appreciate accuracy, clarity and creativity, as well as for those who want to understand how geometric ideas are embodied in the most advanced scientific discoveries and technologies. In general, this edition is not only a textbook, but also a work that can change your perception of mathematics, expand your horizons and inspire new discoveries. In a world where geometry is becoming the key to understanding complex systems and structures, the Course of Differential Geometry (2001-2002) occupies a worthy place among the best educational and scientific sources, opening the door for the reader to an endless and amazing world of manifolds and curves.