The book "Fundamentals of surface theory in tensor presentation" by B. F. Kagan is a fascinating and deep dive into the world of mathematical theory, which will become an indispensable tool for students, graduate students and anyone interested in geometry and physics. In this work, the author offers readers a unique look at complex concepts, using a tensor approach, which makes the material accessible and understandable even for those who are just starting their way in this area. Kagan, known for his work in differential geometry and mathematical physics, masterfully combines theory and practice, which allows the reader not only to learn the basic ideas, but also to see their application in real-world problems. The book covers a wide range of topics, ranging from the basics of tensor analysis to more complex aspects related to surfaces in multidimensional spaces. This makes it an ideal choice for those who want to deepen their knowledge and skills in mathematics. One of the key topics of the book is the study of the properties of surfaces and their interaction with the surrounding space .. Kagan explores concepts such as curvature, geodetic lines, and metrics in detail, allowing the reader to gain a holistic view of surface geometry. Interestingly, the author not only expounds the theory, but also reinforces it with many examples and tasks, which makes the learning process more interactive and exciting. This book will be especially useful for students and graduate students of mathematical and physical faculties, as well as for all those who are engaged in applied mathematics and engineering. If you are interested in topics such as differential geometry, relativity theory or continuum mechanics, then “Fundamentals of surface theory in tensor presentation” will be a real find for you. The book will also be of interest to teachers who are looking for quality materials for their courses. The style of Kagan is clear and logical, which allows the reader to easily assimilate even the most complex concepts. He masterfully uses illustrations and graphics to visualize ideas, which makes the material more visual and accessible. This is especially important in an abstract field such as surface theory, where visual perception plays a key role in understanding. The book "Fundamentals of surface theory in tensor presentation" deserves attention not only for its content, but also for the relevance of the topics it raises. With the rapid development of science and technology, the understanding of geometric foundations is becoming increasingly important. This work helps readers not only to master the theoretical aspects, but also to develop critical thinking and analytical skills that will be useful in any scientific activity. If you are looking for literature that combines depth of analysis and practical applicability, then "Fundamentals of surface theory in tensor presentation" B. F. Kagan is exactly what you need. Immerse yourself in the world of tensor analysis and discover new horizons in the study of mathematics and physics. This book will be your reliable companion on the way to understanding complex geometric structures and their properties, and will also open doors to the exciting world of scientific research.