The book “Fundamentals of combinatorial topology” by Lev Pontryagin is an outstanding work that opens up the world of combinatorial topology, one of the most fascinating and deep areas of mathematics to readers. Pontryagin, known for his outstanding work in the field of topology and algebra, offers readers not just a textbook, but a real intellectual tour, in which every step is thought out and justified. Combinatorial topology studies the properties of spaces that persist under continuous deformations. In his book, Pontryagin introduces the reader to this exciting area, starting with the basics and gradually deepening into more complex concepts. It uses intuitive examples and visual illustrations to make complex ideas understandable. Readers will be able to learn about key concepts such as simplexes, homology, homotopy and many others that play an important role in modern mathematical analysis. This book will be interesting not only for students and graduate students of mathematical faculties, but also for everyone who is fond of mathematics and wants to expand their knowledge in the field of topology. Pontryagin writes with clarity and passion, which makes his work accessible even to those who are not professional mathematicians, but have basic knowledge in this field. If you like to solve puzzles and explore abstract concepts, the “Basics of combinatorial topology” will become a real storehouse of knowledge for you. The topics raised in the book cover a wide range of issues related to topology, including the study of the properties of spaces that are independent of their specific representation. Pontryagin emphasizes the importance of combinatorial methods in topology, which makes his work especially relevant in light of modern research. It shows how combinatorial approaches can be applied to solve various problems, which makes the book not only theoretical, but also practical. Pontryagin's style is clear and logical, which allows the reader to easily follow his thoughts. He skillfully combines strict mathematical formulation with available explanations, which makes his text lively and fascinating. Pontryagin is also known for his other works, such as "