"Geometry of linear manifolds in n-dimensional space" is an outstanding work written by the famous Russian mathematician Igor Mikhailovich Jagl .. The book is a deep dive into the world of linear algebra and geometry, revealing to the reader complex concepts and ideas that may seem inaccessible at first glance. However, the style of presentation of the author makes even the most abstract topics understandable and fascinating. In this book, Yaglom explores linear manifoldsobjects that occupy a central place in multidimensional geometry. The reader will get acquainted with the main properties and characteristics of these varieties, as well as with their applications in various fields of mathematics and physics. The author not only explains the theoretical aspects, but also offers many examples and tasks, which makes the material more accessible to perception. Each chapter of the book is imbued with logic and consistency, which allows the reader to master complex concepts step by step. The book will be of interest to both students and teachers, as well as everyone who is fond of mathematics and wants to deepen their knowledge in the field of geometry and linear algebra. It is suitable for readers who are at the level of higher education, as well as for those who are engaged in self-education. If you are interested in topics such as multidimensional spaces, vectors, matrices and their application in real life, then this work will be a real find for you. The topics raised in the book cover a wide range of issues, from the basics of linear algebra to more complex concepts such as projective and affine spaces. Yaglom focuses on the relationship between algebraic and geometric aspects, which allows the reader to see mathematics as a whole. This is not just a textbook, but a real philosophy of mathematics, where each formula and theorem has its place and meaning. Jaglom's style is clear and logical, which makes his books particularly valuable for study. He is known for his work in mathematics, among which can be distinguished "