The Theory of Volterra Operators in Hilbert Space and Its Applications by Hochberg I. C. and Crane M. G. represents a significant contribution to the field of functional analysis and operator theory. This edition will be of particular interest to those seeking to deepen their knowledge in mathematics, as well as those working in related fields such as physics, engineering, and computer science. The book focuses on volteric operators, an important class of linear operators that play a key role in the theory of integral equations. The authors carefully examine their properties, methods of analysis and applications in various contexts, which makes this work an indispensable tool for students, graduate students and researchers engaged in mathematical modeling and theoretical aspects of analysis. The book begins with the basics of the theory of volteric operators, introducing the reader to the world of Hilbert spaces and their features. Gohberg and Crane not only explain the basic concepts, but also offer the reader a number of examples and tasks that help to consolidate the knowledge gained. This makes the book accessible and understandable even for those who are just starting to get acquainted with this topic. One of the key topics addressed in the book is the relationship between volteric operators and different types of integral equations. The authors demonstrate how these operators can be used to solve real problems, which makes the material especially relevant for practitioners. Readers will be able to see how the theory finds application in areas such as control theory, signal processing, and numerical methods. The book also raises important questions about the existence and uniqueness of solutions of integral equations, which is a fundamental aspect for many scientific studies. Gochberg and Crane focus on modern methods of analysis, which allows the reader not only to learn the theoretical foundations, but also to get acquainted with the latest achievements in this field. The style of the authors is distinguished by clarity and logical presentation, which makes the material available to a wide audience. Gohberg I. C. and Crane M. G. are known for their work in functional analysis and operator theory, and their expertise allows them to share knowledge at a high level. Their previous publications have also earned recognition in the scientific community, and this book is no exception. Who can like this edition? First, it will be useful for students of mathematical and physical faculties, as well as graduate students who are looking for a deep and systematic presentation of the topic . Secondly, researchers and practitioners working in the field of applied mathematics will find in the book many ideas and methods that will help them in their scientific and professional activities. Finally, the book will be of interest to anyone who wants to expand their knowledge in the field of operator theory and integral equations. Thus, “The Theory of Volterra Operators in Hilbert Space and Its Applications” is not just a textbook, but a real encyclopedia of knowledge that opens the door to a world of complex and fascinating mathematics. If you are looking for a book that will help you deepen your knowledge and expand your horizons in functional analysis, this edition will be an excellent choice for you.