The book "Tasks and exercises on functional analysis: a textbook" by Trenogin B. A. and his colleagues is an indispensable resource for students, graduate students and teachers seeking to understand and master the complex concepts of functional analysis This textbook not only contains theoretical calculations, but also offers readers a variety of tasks and exercises that will help to consolidate the knowledge gained and develop skills in solving practical problems. Functional analysis is the field of mathematics that investigates functionals and their properties, as well as their application in various fields of science and technology. Trenoggin's book covers a wide range of topics, ranging from the basics of functional analysis to more complex concepts such as Banach and Hilbert spaces, operator algebras, and spectral theory. Each chapter contains carefully selected tasks that range from simple to more complex, allowing the reader to gradually delve into the material. This book will be especially useful for students of mathematical and physical faculties, as well as for those who are preparing for exams or research in the field of mathematics. It is suitable for both beginners and more experienced readers who want to refresh their knowledge or prepare for more complex topics. If you are interested in areas such as applied mathematics, control theory, quantum mechanics or statistics, this guide will be a reliable assistant for you. One of the main topics raised in the book is the importance of practical application of the theory. The authors emphasize that without practice, even the most complex theoretical concepts can remain misunderstood. Each exercise is accompanied by detailed comments and decisions, which allows the reader not only to test their knowledge, but also to understand how to apply the theory in practice. This makes the tutorial especially valuable for those who want not only to learn formulas, but also to be able to use them in real tasks. The style of Trenoggin and his co-authors is clear and accessible, which allows even complex mathematical concepts to be presented in an understandable form. Their experience and deep understanding of the subject make the book not only a textbook, but also a real guide to the world of functional analysis. In addition, the authors offer readers a lot of additional materials and links to other well-known works, which allows you to deepen your knowledge and expand your horizons. If you’re looking for a tutorial that combines theory and practice, “Functional Analysis Tasks and Exercises” is exactly what you need. The book will be a great addition to your learning materials and will help you move confidently along the path of learning functional analysis. Do not miss the opportunity to discover this fascinating and important branch of mathematics, which finds application in a wide variety of fields of science and technology.