The book “Fundamentals of combinatorial topology” by Lev Pontryagin is an outstanding work that has become a classic in the field of mathematics and topology theory. Pontryagin, known for his in-depth research in algebraic and combinatorial topology, offers the reader a unique perspective on this complex but fascinating discipline. In his book, he aims to make combinatorial topology accessible to a wide audience, including undergraduates, graduate students, and anyone with an interest in mathematics. The book covers the basic concepts and methods of combinatorial topology, starting with simple concepts and ending with more complex topics. Pontryagin masterfully explains how combinatorial structures can be used to study topological spaces, and demonstrates how these ideas are applied in various areas of mathematics. The reader will get acquainted with such important concepts as simplicial complexes, homology and cohomology, as well as with the basics of knot and manifold theory. Each chapter of the book is permeated with deep reflections of the author, who not only shares knowledge, but also inspires the reader to further research. This book will be of interest not only to mathematicians, but also to everyone who is passionate about scientific research and seeks to understand how different fields of science can intersect. Senior students, graduate students and teachers will find it useful materials for their research and lectures . It will also be useful for those who want to expand their knowledge in the field of modern mathematics and learn about new approaches to solving old problems. The topics raised in the book cover a wide range of issues related to combinatorial topology. Pontryagin discusses not only theoretical aspects, but also practical applications of his ideas. It shows how combinatorial topology can be used to solve real-world problems, making the book particularly valuable for those seeking practical application of their knowledge. This work is not just a textbook, but a real guiding star for everyone who wants to plunge into the world of mathematics and discover new horizons. The style of Pontryagin is distinguished by clarity and logical presentation. He skillfully combines strict mathematical formulation with accessible language, which allows the reader to easily follow his thoughts. This makes the book not only useful, but also fascinating to read. Pontryagin is also known for his other works, such as Basics of Algebraic Topology and Topology, which are also noteworthy and may be of interest to those who want to deepen their knowledge in this field. If you are looking for a book that will help you understand the basics of combinatorial topology, or want to expand your horizons in mathematics, “Basics of combinatorial topology” by Lev Pontryagin is exactly what you need. It will become a reliable companion on your way to understanding complex mathematical concepts and will open up new opportunities for scientific research. Do not miss the chance to get acquainted with this outstanding work, which has been inspiring and educating students and researchers around the world for many years.