The Topological Library . Volume 1. Cobordisms and Their Applications" is an outstanding work that immerses the reader in the world of topology, one of the most fascinating and complex areas of mathematics. Authors, including such eminent scientists as Lev Semenovich Pontryagin, Tom R. and Sergey Petrovich Novikov, create a unique synthesis of theory and practice, which will be of interest to both professional mathematicians and students seeking to deepen their knowledge in this area. The first part of the "Topological Library" focuses on cobordisms - a concept that explores the relationship between diversity and its boundaries. The authors consider in detail various aspects of cobordism, starting with its foundations and ending with modern applications in mathematics and related sciences. The reader will be able to learn how cobordisms affect the understanding of the topological properties of manifolds and how they can be used to solve complex problems in homotopy theory and differential geometry. This book will be especially interesting for those who are fond of mathematics, physics and even philosophy. Senior students, graduate students and teachers will find in it not only theoretical calculations, but also practical examples that will help to better assimilate the material. It will also be a useful resource for researchers working in topology and its applications in other sciences, such as computer science and biology. The topics raised in the book cover a wide range of issues, including the classification of varieties, the study of their properties, and the application of cobordisms to various mathematical problems. The authors not only share their knowledge, but also open new horizons for future research, which makes this work relevant and in demand in the scientific community. Lev Semenovich Pontryagin, one of the authors, is known for his significant contributions to the topology and theory of functional spaces. His works, such as Basics of General Topology, have become classics and have influenced generations of mathematicians. In the "Topological Library" readers will be able to see how his ideas are developed and applied in modern research. Tom R. and Sergey Petrovich Novikov, also recognized authorities in the field of mathematics, add their unique views and approaches to the book, which makes it multifaceted and interesting. The style of the authors is clear and accessible, which allows even complex concepts to be explained in simple language. Each section of the book is logically structured, which helps the reader gradually immerse himself in the material and master it. At the same time, despite the scientific approach, the authors do not forget that mathematics is not only formulas and theorems, but also an art that requires creativity and intuition. If you are looking for literature on topology that combines theoretical foundations and practical applications, then the “Topological Library. Volume 1. Cobordisms and their applications" will be a real find for you. This book will not only expand your knowledge, but also inspire new research and discoveries in the world of mathematics. Do not miss the opportunity to get acquainted with the work of outstanding scientists and immerse yourself in the fascinating world of cobordisms!