The Geometry of the Lie Groups . Symmetric, Parabolic and Periodic Spaces” by B. A. Rosenfeld and M. P. Zamakhovsky is a fascinating and in-depth study in the field of differential geometry and group theory. This work will be a real discovery for both students and professionals interested in mathematics and physics, as well as for all who seek to expand their knowledge of the complex structures that shape our understanding of space and symmetry. In this book, the authors explore Li groups and their geometric properties, plunging the reader into the world of symmetric, parabolic, and periodic spaces. From the first pages you will feel how the authors masterfully combine theoretical concepts with practical examples, which makes the material accessible and understandable. They not only explain the basic principles, but also offer the reader the opportunity to independently understand complex issues, such as the classification of symmetric spaces and their application in various fields of science. This book will be especially interesting for those who are fond of mathematics, physics, as well as related disciplines, such as computer science and engineering. Students and graduate students studying differential geometry will find valuable materials in it to prepare for exams and write scientific papers. Professionals working in the field of theoretical physics will be able to use the acquired knowledge to deepen their understanding of symmetry in physical systems. The topics raised in the book cover a wide range of issues, including the study of the structure of Lie groups, their representations and actions on various geometric objects. The authors focus on the importance of symmetry in mathematics and physics, showing how it can be used to solve complex problems. The reader will be able to learn about how symmetric spaces affect physical theories such as relativity and quantum mechanics. The style of the authors is distinguished by clarity and logical presentation, which makes it easy to assimilate even the most complex concepts. B. A. Rosenfeld and M. P. Zamakhovsky is known for his scientific works and research in mathematics, and their experience and in-depth knowledge make this book a valuable resource for anyone who wants to immerse themselves in the world of geometry and Lie groups. Their previous work is also noteworthy, and many readers who have appreciated Lee's Group Geometry may be interested in their other publications related to mathematical physics and group theory. The Geometry of the Lie Groups . Symmetric, Parabolic and Periodic Spaces" is not just a textbook, but a real find for anyone who wants to understand how mathematics and physics are intertwined in the study of symmetry and the structure of space. It will become a reliable companion on your scientific journey, opening the door to new knowledge and ideas. If you are looking for literature that combines deep theoretical analysis and practical application, then this book should definitely take its rightful place on your shelf.