The book "Special functions and theory of representations of groups" by H. I. Vilenkina is a unique and in-depth study that immerses the reader in the world of mathematical analysis and group theory. This work will be a real discovery for students, graduate students and teachers, as well as for anyone interested in modern areas in mathematics and physics. Vilenkin, known for his outstanding work in the field of mathematical analysis, offers in his book an original view of special functions that play a key role in various fields of science. It not only describes the theory of group representations, but also shows how these representations can be used to study special functions. This makes the book particularly valuable for those seeking to understand how abstract mathematical concepts can be applied in practice. The book covers a wide range of topics, ranging from the foundations of group theory to more complex aspects, such as representations of continuous groups and their application in quantum mechanics. Vilenkin masterfully combines theory and practice, which allows the reader not only to assimilate the material, but also to see its application in real problems. This makes the book ideal for undergraduate and graduate students studying mathematics, physics, and engineering sciences. Topics raised in the book range from basic concepts of group theory to complex mathematical constructs such as Bessel functions, Legendre polynomials, and other special functions. Vilenkin pays attention not only to theoretical aspects, but also to practical applications, which makes his work especially relevant for researchers and practitioners. The reader will be able to see how theoretical concepts are reflected in real problems, which, of course, adds value to this publication. The book will be of interest not only to mathematicians, but also to physicists, engineers and everyone who works in the field of applied mathematics. It will become an indispensable tool for those who want to deepen their knowledge in the field of special functions and group representation theory. Thanks to an accessible style of presentation and a clear structure, both beginners and experienced readers will be able to easily navigate the material. Style N. I. Vilenkina is clear and logical, which makes his work especially attractive to a wide audience. His other well-known works, such as Analysis on Diversity and Theory of Representations and Special Functions, are also noteworthy and may be useful as a supplement to the study of the topics covered in this book. Vilenkin skillfully combines theory and practice, which allows the reader not only to learn the material, but also to see its application in real problems. If you are looking for a book that will help you understand complex mathematical concepts and also teach you how to put them into practice, “Special Functions and Group Representation Theory” is exactly what you need. This work will become a reliable companion in your mathematical journey, opening up new horizons of knowledge and opportunities for you. Do not miss the chance to immerse yourself in the world of mathematics with H. I. Vilenkin and discover the amazing connections between abstract concepts and real-world applications!