The book “Geometric methods of nonlinear analysis” by Mikhail Alexandrovich Krasnoselsky and Pavel Petrovich Zabreiko is an outstanding work that opens up for readers a fascinating world of mathematical analysis focused on nonlinear problems. This work not only delves into the theoretical foundations, but also offers practical tools that can be useful to both students and professional mathematicians. The focus of the book is on geometric methods that allow you to explore and solve complex nonlinear problems. The authors, with deep knowledge and experience, share their findings and approaches that make nonlinear analysis more accessible and understandable. The book covers a wide range of topics, including topology, functional analysis, and optimization techniques, allowing the reader to see how geometric ideas can be applied to solve real-world mathematical problems. This book will be interesting not only for students and graduate students of mathematical and physical specialties, but also for specialists working in the field of applied mathematics, engineering and even economics. If you are passionate about mathematics and strive to understand more deeply nonlinear systems, the “Geometric methods of nonlinear analysis” will become a real treasure for you. It is suitable for those who are just beginning their journey in mathematics, and for experienced researchers who want to expand their knowledge. The topics raised in the book are relevant and important for the modern scientific community. Nonlinear equations and systems play a key role in fields ranging from physics to biology, from economics to engineering. Understanding geometric methods allows not only to solve theoretical problems, but also to apply the knowledge gained in practice. The authors focus on how visualization and geometric representations can facilitate the understanding of complex processes, making their approach particularly valuable. The style of Krasnoselsky and Zabreiko is clear and logical . They are able to explain complex concepts in simple and accessible language, which makes the book not only useful, but also fascinating to read. Their previous work, such as "Functional Analysis Methods in Nonlinear Analysis Tasks" and "Nonlinear Equations and Their Applications", have also gained recognition and have become foundational in their field. In Geometric Methods of Nonlinear Analysis, the authors continue to develop their ideas, offering readers new approaches and solutions. The book not only enriches the reader with knowledge, but also inspires further research. It can be an excellent addition to the library of anyone interested in mathematics, and will also be useful to teachers and students who want to deepen their knowledge in the field of non-linear analysis. In it you will find many examples, tasks and illustrations that will help you better absorb the material and apply it in practice. If you are looking for literature on mathematical analysis, nonlinear equations or geometric methods, then “Geometric methods of nonlinear analysis” is exactly what you need. This book will not only expand your horizons, but also help you look at familiar things from a new angle. Do not miss the opportunity to get acquainted with the work of two outstanding scientists who have made a significant contribution to the development of mathematical science.