Book "Semigroups and groups of operators with nuclei. The textbook by Vladimir Evgenievich Fedorov is a fascinating and deep immersion in the world of mathematical analysis and operator theory, which will become an indispensable assistant for students, graduate students and specialists in mathematics and physics. This work not only serves as a textbook, but also represents an important contribution to the development of the theoretical framework necessary for understanding complex mathematical concepts. In his manual, Fedorov explores semi-groups and groups of operators that play a key role in various fields of science, including quantum mechanics, control theory, and mathematical physics. The author carefully explains the basic concepts and properties of these mathematical objects, focusing on their application in real-world problems. The book begins with the basics, gradually deepening into more complex topics, which allows the reader not only to learn the material, but also to develop analytical thinking. One of the main features of the book is its accessibility to a wide audience. Thanks to a clear and logical style of presentation, even those who are just starting their way in mathematics will be able to find useful knowledge in it. However, this does not mean that experienced professionals will not find for themselves an interesting . On the contrary, Fedorov’s in-depth analysis and original approaches to solving problems will allow even the most sophisticated readers to open new horizons in their scientific activities. The book raises many topical topics, such as the structure of operators, their spectral properties, and applications in various mathematical models. Fedorov is not limited to only the theoretical part, it also includes practical examples and tasks, which makes studying the material more exciting and useful. The reader will be able not only to get acquainted with the theory, but also to apply the knowledge gained in practice, which is especially important for students and graduate students. If you are interested in topics such as functional analysis, differential equations or mathematical physics, this manual will be a real find for you. It will help you better understand complex concepts and learn how to apply them in a variety of scientific and practical tasks. The book will be useful for both undergraduate and graduate students preparing for the defense of dissertations, as well as for teachers looking for quality materials for their lectures. The style of Vladimir Evgenievich Fedorov is clear and logical, which makes his work easy to perceive. He is known for his research in operator theory and functional analysis, and his previous publications have also gained recognition in the scientific community. The book Semigroups and Operator Groups with Kernels continues this tradition by offering readers not only theoretical knowledge but also practical skills that will be useful in their future careers. Thus, "Semigroups and groups of operators with nuclei. The textbook is not just a book, but a whole world in which everyone who wants to expand his knowledge in mathematics and its applications should immerse himself. This work will become a reliable companion for all who seek new discoveries and want to deepen their knowledge in complex but fascinating topics. Do not miss the opportunity to get acquainted with this unique work, which can change your view of mathematics and its possibilities!