The book “Variational methods in quantum theory of atomic systems: a textbook” by Evgeny Cheglokov represents a unique contribution to the field of quantum physics and theoretical chemistry . This manual will become an indispensable assistant for students, graduate students and teachers engaged in the study of atomic systems and their interaction. While many textbooks focus on the general principles of quantum mechanics, Cheglokov's work delves into specific aspects of variational methods that are key to understanding complex quantum systems. The book begins with the basics, explaining what variational methods are and how they are applied in quantum mechanics. The reader is immersed in the world of mathematical formulas and physical concepts, which at first glance may seem complicated, but thanks to the clear and accessible style of the author, they become understandable even for those who are just starting their way in this area. Cheglokov masterfully combines theory with practical examples, which allows readers not only to learn the material, but also to see its application in real problems. One of the main themes of the book is the use of variational methods to find approximate solutions to the Schrdinger equation. Cheglokov examines in detail various approaches, including the method of variational energy estimation, which allows readers to understand how to effectively solve problems that are not amenable to analytical solution. This topic will be especially interesting for those who want to deepen their knowledge in the field of computational quantum mechanics and theoretical physics. The book also touches on important aspects, such as the interaction of atoms with external fields, making it relevant to researchers working in atomic and molecular physics. Readers will be able to learn about the latest advances in this field and how variational methods help in the development of new technologies, such as quantum computers and nanomaterials. "Variational methods in quantum theory of atomic systems" will be of interest not only to students and graduate students, but also to experienced researchers who want to refresh their knowledge or find new approaches to solving complex problems. The book is suitable for those who are fond of physics, chemistry and related sciences, as well as those who work in the field of materials science and nanotechnology. It can be an excellent addition to the library of any scientist seeking a deep understanding of quantum processes. The style of Yevgeny Ivanovich Cheglokov is distinguished by clarity and logic. He skillfully combines theoretical calculations with practical examples, which makes the material accessible to perception. Readers familiar with his other works will appreciate the consistency and depth of the presentation, which became the author's calling card. Cheglokov is also known for his research in the theory of multiparticle systems and interactions, which gives his works additional value. This book is not just a textbook; it is a real guide to the world of quantum mechanics, which will help readers not only to master the theory, but also to learn how to apply it in practice. If you are looking for literature that will help you understand the complex aspects of quantum theory and teach you how to use variational methods to solve real-world problems, then “Variational Methods in Quantum Theory of Atomic Systems” will be your reliable companion on this fascinating journey.