The Differential Geometry and Topology . Troitsky’s course of lectures is a fascinating and deep dive into the world of mathematical concepts that form the basis for understanding complex structures in geometry and topology. This publication will be an indispensable assistant for both students and teachers seeking to master these important sections of mathematics. In his book, Troitsky offers readers not just a set of theoretical knowledge, but also the practical application of this knowledge in various fields of science and technology. He begins with the basics, gradually introducing more complex concepts, which makes the material available to a wide range of readers. The book covers key topics such as curvature, manifolds, topological spaces and their properties, as well as various methods used in differential geometry. Each section is riddled with examples and tasks that help to consolidate the knowledge gained and develop analytical thinking. This book will be especially interesting for students of mathematical, physical and engineering faculties, as well as graduate students and researchers working in the field of mathematics and related disciplines .. If you are interested in mathematics, love to solve complex problems and want to understand how geometry and topology affect our perception of space, then “Differential geometry and topology” will be a real discovery for you. The topics raised in the book go beyond pure mathematics and touch on philosophical aspects related to the perception of space and form. Troitsky not only expounds facts, but also raises important questions about how we can interpret and use these mathematical concepts in real life. This makes the book not only a textbook, but also a source of inspiration for reflection on the nature of mathematics and its role in our world. The style of the author is distinguished by clarity and logical presentation, which allows the reader to easily follow the thought and assimilate even the most complex ideas. Troitsky uses many illustrations and graphics, which makes the material more clear and understandable. His approach to learning is based on the principle of gradual complication, which allows the reader to confidently move from simple to complex, without losing interest in the material being studied. The Differential Geometry and Topology . The course of lectures” is part of the broader context of Troitsky’s work, which is also known for its publications on mathematical analysis and algebra. If you are interested in works such as "