The book "Application of group theory in quantum mechanics" by Petrashen M. and . and Trifonov E. D. is a fascinating and in-depth study at the intersection of mathematics and physics, which will be a real find for students, graduate students and anyone interested in modern advances in quantum mechanics. This work not only highlights key aspects of group theory, but also demonstrates their importance and application in quantum systems, making it an indispensable tool for those seeking to understand the complex concepts behind the behavior of microparticles. The book begins with the foundations of group theory, gradually introducing the reader to the world of symmetries and their role in physics. The authors masterfully explain how symmetries affect physical laws and how they help simplify complex problems arising in quantum mechanics. This makes the material available even to those who do not have a deep knowledge of mathematics, but are ready to plunge into the fascinating world of quantum phenomena. Interestingly, the authors use many examples and tasks, which allows the reader not only to assimilate theoretical material, but also to apply it in practice. Who will like this book? First of all, it will be of interest to students of physics and mathematics, as well as graduate students working in the field of theoretical physics . However, interest in it can be shown by wider circles of readers, including teachers, researchers and even science lovers who want to expand their knowledge about the quantum world. If you are looking for literature that will help you understand complex concepts and give you the opportunity to look at quantum mechanics from a new angle, then the “Application of group theory in quantum mechanics” will be a real discovery for you. The topics raised in the book cover a wide range of issues related to symmetry, invariance, and their applications in quantum systems. The authors not only explain the theoretical foundations, but also show how these ideas find their application in real-world physical problems such as spin systems, atomic and molecular structures, and field theory. This makes the book relevant not only for the academic environment, but also for practical research, which emphasizes its importance in modern scientific discourse. The style of the authors is distinguished by clarity and logical presentation, which allows the reader to easily follow the course of thought and understand the material presented more deeply. Petrashen and Trifonov, being experienced researchers and teachers, understand perfectly how important it is to make complex ideas accessible and understandable. Their previous work also deserves attention, as they have repeatedly raised important issues in the field of theoretical physics and mathematics, which confirms their high level of expertise and dedication. If you’re looking for books on quantum mechanics that will help you better understand group theory and its applications, you might want to look at works like Dirac’s Quantum Mechanics or G.’s Group Theory in Physics. G. Gurvich . However, the “Application of Group Theory in Quantum Mechanics” stands out for its unique presentation of material and practical approach, making it an indispensable resource for anyone who wants to delve into this exciting and complex field of science. Thus, the book Petraen M. and . and Trifonov E. D. This is not just a textbook, but a real guide star for everyone who seeks to understand and master quantum mechanics through the prism of group theory. Do not miss the opportunity to enrich your knowledge and discover new horizons in the world of science!