The book "The problem of substantiation of geometry in a modern formulation" by B. F. Kagan is a fascinating and profound study that immerses the reader in the world of geometry, considering it not only as a set of theorems and axioms, but also as a living, developing science. In this work, the author sets himself an ambitious task - to substantiate geometric principles using modern mathematical approaches and theories, which makes the book relevant and interesting for both students and professionals in the field of mathematics. Kagan, known for his work in mathematical logic and geometry, offers readers a fresh perspective on traditional problems that have troubled the minds of scientists for centuries. He addresses the main questions related to the axiomatic approach to geometry and explores how modern mathematical theories can help in their solution. The book deals with topics such as the relationship between geometry and topology, the role of symmetry in geometric constructions, and many other aspects that make geometry more accessible and understandable. This book will be especially interesting for those who are fond of mathematics, physics and philosophy of science. Students and teachers, as well as researchers working in the field of mathematics, will find in it many useful ideas and concepts. In. F. Kagan appeals to readers with deep respect and a desire to explain complex things in simple language, which makes his work available even to those who are just starting their way in the study of geometry. One of the key themes of the book is the question of how modern science can rethink and substantiate classical geometric concepts. Kagan is not afraid to question established ideas and proposes new approaches that can change our understanding of geometry. His style of presentation is clear and logical, which allows the reader to easily follow the idea of the author and immerse themselves in the issues discussed. The book "The task of substantiating geometry in the modern formulation" not only expands the horizons of understanding geometry, but also raises important philosophical questions about the nature of science and its development. Kagan touches on topics that relate not only to mathematics, but also to the broader aspects of human knowledge, which makes this work multifaceted and profound. If you are looking for literature that combines scientific rigor and philosophical reflection, then this book will be an excellent choice. It can be of interest not only to students and teachers, but also to anyone who seeks to understand how scientific ideas develop and how they can be applied in various fields of knowledge. Kagan is also known for his other works that deal with mathematical logic and set theory, and his style is always distinguished by depth of analysis and a desire for clarity. Reading "The Problem of Grounding Geometry in a Modern Setting", you can not only deepen your knowledge in the field of geometry, but also enjoy the process of cognition, which makes this book a real find for lovers of science and mathematics. Thus, “The Problem of Substantiating Geometry in a Modern Setting” is not just a textbook, but a real intellectual adventure book that invites you to the world of mathematical discoveries and deep reflections. Do not miss the opportunity to touch this fascinating study, which can change your idea of geometry and its place in the modern world of science.