The book “Orthogonal polynomials” by Alexandrov is a fascinating and in-depth study that immerses the reader in the world of mathematical analysis and function theory. In this work, the author not only explains the basic concepts of orthogonal polynomials, but also reveals their application in various fields of science and technology. This makes the book interesting not only for undergraduate and graduate students studying mathematics, but also for professionals working in related fields such as physics, computer science, and engineering. Aleksandrov, known for his deep knowledge and ability to explain complex topics easily, offers readers a unique perspective on orthogonal polynomials, which are an important tool in mathematical analysis and probability theory. These polynomials find application in a variety of problems, including the approximation of functions, the solution of differential equations, and even in quantum mechanics. The book covers both theoretical aspects and practical examples, which allows the reader not only to understand, but also to apply the knowledge gained in practice. For whom is this book intended? First of all, it will be of interest to students of mathematical and physical faculties, graduate students and teachers, as well as anyone who is fond of mathematics and wants to deepen their knowledge in this area . However, due to the available style of presentation and many examples, the book can be useful for those who are just beginning to get acquainted with mathematical analysis. There is no excessive formalization in it, which makes the material more understandable and easier to perceive. The topics raised in the book are diverse and relevant. Alexandrov discusses not only the theory of orthogonal polynomials, but also their relationship to other mathematical concepts, such as probability theory and functional analysis. The book also addresses issues related to the use of orthogonal polynomials in numerical methods, making it particularly valuable for practitioners. The reader will be able to see how abstract mathematical ideas find their application in real problems, which adds additional value to the work. Alexander's style is clear and logical. It skillfully combines theoretical calculations with practical examples, which allows the reader not only to assimilate the material, but also to see its application in action. This approach makes the book not only a textbook, but also a fascinating reading for anyone interested in mathematics. In his work, you can notice the desire for accessibility and understanding of complex ideas, which makes his work in demand among a wide audience. If you’re looking for books on mathematical analysis, function theory, or numerical methods, Alexandrov’s Orthogonal polynomials will be a great addition to your library. This work will not only expand your knowledge, but also inspire further research in the field of mathematics. Do not miss the opportunity to immerse yourself in the world of orthogonal polynomials and discover new horizons in mathematical analysis!