The book "Application of group theory in quantum mechanics", written by famous scientists Petrashen M. and . and Trifonov E . D. It is a fascinating and deep dive into one of the most complex and interesting areas of physics. This work will be especially useful for students, graduate students and researchers interested in both theoretical physics and mathematics, as it not only explains complex concepts, but also demonstrates their practical application. In this book, the authors consider how group theory, one of the most important branches of mathematics, finds its application in quantum mechanics. The reader will be able to learn how symmetries and transformation groups help explain physical phenomena at the quantum level. It is not just a textbook it is a real laboratory of ideas, where mathematical constructions come to life, and physical laws become more understandable and accessible. The book begins with the basics of group theory, which makes it accessible even to those who do not have in-depth knowledge in this field. Gradually, the authors introduce the reader to more complex concepts, such as group representations and their relationship to quantum states. Each chapter is filled with examples and tasks that help to consolidate the material and develop analytical thinking. The book focuses on how theoretical constructs are reflected in real-world physical systems. For example, the authors discuss the application of group theory in the study of atomic and molecular structures, as well as in quantum field theory. This makes the book not only a theoretical, but also a practical guide, which is especially important for students and practicing physicists. Who can like this work? First of all, it will be interesting for students and graduate students of physics and mathematics, as well as teachers who are looking for quality materials for their courses . In addition, the book will be useful to anyone interested in modern physical theories and wants to deepen their knowledge in the field of quantum mechanics and mathematical methods used in this science. The topics raised in the book go beyond just studying group theory. The authors discuss the philosophical aspects of symmetry in nature and its role in the formation of physical laws. This makes the book not only a textbook, but also a source for reflection on the nature of reality and how we perceive the world around us. The style of Petrashen and Trifonov is distinguished by clarity and logical presentation . They are able to explain complex things in simple language, which makes their work available to a wide audience. Both authors have extensive experience in teaching and research, which allows them to share their knowledge and findings with readers. Their previous work has also been popular among students and researchers, and this book will not be an exception. If you are looking for literature that will help you understand the complex concepts of quantum mechanics and group theory, “Applying Group Theory in Quantum Mechanics” will be your reliable companion on this fascinating journey. Do not miss the opportunity to discover a world where mathematics and physics are intertwined, creating amazing and sometimes unexpected results. This book is your key to understanding the complex phenomena that shape our universe.