The book "Fundamentals of the theory of calculations" by author E. Kaleeva is a fascinating and deep immersion into the world of computational processes, which will become an indispensable tool for both students and professionals in the field of computer science and mathematics. This work not only explains the basic concepts of computational theory, but also opens the door to the world of algorithms, automata and formal languages, which makes it relevant for anyone interested in the basics of computer science. Kaliev in his book masterfully combines theoretical aspects with practical examples, which allows the reader not only to assimilate the material, but also to see its application in real-world problems. He begins with the basics, explaining concepts such as computability and complexity, and gradually delves into more complex topics such as the incompleteness theorem and Russell's paradox. At the same time, the author uses an accessible language, which makes complex ideas more understandable and easy to perceive. This book will be of particular interest to undergraduate computer science students, as well as graduate students and researchers working in the field of computational theory. It can also attract the attention of professionals seeking to update their knowledge or deepen their understanding of computational processes. If you are interested in topics such as algorithms, programming, artificial intelligence, or even the philosophy of computing, the Fundamentals of Computational Theory will be a real discovery for you. One of the key topics raised in the book is the question of computability limits. Kaliev not only explains what computable functions are, but also considers what problems cannot be solved with algorithms. This raises important philosophical questions about the nature of knowledge and the capabilities of the human mind. The reader will be able to think about what it means to "calculate" and what restrictions exist in this area. The author's style is clear and logical, which makes it easy to follow his thought. Kaliev uses many illustrations and examples to make the material more visual. His approach to learning is based on the principle of "from simple to complex", which helps the reader gradually master increasingly complex concepts. In this respect, the book is reminiscent of such works as “Algorithms: construction and analysis” of Kormen.