The book “Zeta function” by Igor Romanovich Shafarevich is a fascinating and in-depth study of one of the most mysterious and significant mathematical concepts, which for centuries has attracted the attention of scientists and mathematics lovers. In this work, the author offers the reader not only the theoretical foundations of the zeta function, but also its practical application in various fields of science, including number theory and mathematical physics. Shafarevich, known for his outstanding work in algebraic geometry and number theory, creates a unique atmosphere in which mathematics becomes not just a set of formulas and theorems, but a real art. His style of presentation is clear and accessible, which makes complex concepts understandable even for those who are not professional mathematicians. In the "Zeta function" he masterfully combines a strict scientific approach with a fascinating narrative, which allows the reader not only to assimilate the material, but also to really get interested in the subject. The book will be of particular interest to students and teachers of mathematical faculties, as well as to anyone who is fond of mathematics and wants to deepen their knowledge in the field of number theory. If you are looking for literature that will help you understand how the zeta function is related to the distribution of prime numbers or how it is used in modern research, then this work will be a real find for you. In addition, fans of scientific popularization and probability theory will also find the book a lot of useful and fascinating. One of the central themes of the book is a puzzle known as the Riemann hypothesis, which is associated with zeta-function zeros. Shafarevich not only explains what it is, but also immerses the reader in the context of the historical development of this hypothesis, telling about the great mathematicians who tried to prove it. This creates not only a scientific but also a cultural context, allowing the reader to see how mathematics interacts with history and philosophy. Shafarevich also touches on issues related to the application of zeta function in quantum physics and other fields of science. It shows how mathematical concepts can be used to solve real-world problems, making the book relevant and useful for researchers and practitioners. This multi-layered themes and approaches makes the "Deta function" not just a textbook, but a real guide to the world of mathematics. If you are already familiar with other works of Shafarevich, such as "Fundamentals of algebraic geometry" or "