Elements of Field Theory: Variational Symmetries and Geometric Invariants, written by B. A. Kowalev and Y. N. Radayev, is a unique and in-depth study in the field of mathematical physics that will be of interest to both professional scientists and students seeking to deepen their knowledge in this complex but exciting field. The authors, possessing rich experience and deep knowledge, offer the reader to plunge into the world of variational symmetries and geometric invariants, which are the cornerstones of modern field theory. The book begins with the basics, gradually introducing the reader to more complex concepts, which makes it accessible even to those who are just beginning their journey in this area. However, despite its accessibility, the work does not lose in depth and scientific rigor, which makes it a valuable resource for more experienced researchers. The topics covered in the book cover a wide range of issues, including fundamental aspects of symmetry in physics, methods of variational calculus, and their application in the context of field theory. The authors emphasize the importance of geometric invariants, which play a key role in understanding physical systems and their behavior. The reader will be able to learn how these concepts intersect and interact, creating a holistic view of field theory. This book will be of particular interest to undergraduate and graduate students studying physics, mathematics, and related disciplines. It will also be a useful tool for teachers who want to deepen their knowledge and expand their training programs. Researchers working in the field of theoretical physics will find in it many useful ideas and approaches that can be applied in their own work. The style of the authors is distinguished by clarity and logical presentation, which allows the reader to easily follow the course of thought and assimilate complex concepts. Kovalev and Radaev use many examples and illustrations that help illustrate key ideas and make the material more visual. This makes the book not only informative, but also fascinating to read. In addition, "Elements of field theory" may be of interest to those who are looking for parallels with other works in the field of mathematical physics. Readers familiar with the works of authors such as Richard Feynman or Lev Landau will find in this book many cross topics and ideas that will enrich their understanding of the subject. The book opens new horizons for those who want not only to study physics, but also to understand it at a deeper level. In conclusion, “Elements of field theory: variational symmetries and geometric invariants” is not just a textbook, but a real find for anyone interested in modern trends in theoretical physics. It offers the reader the opportunity not only to get acquainted with the basics, but also to delve into the complex but fascinating aspects of field theory. If you are looking for a book that will help you expand your knowledge and look at physics from a new perspective, this edition will be an excellent choice.