The book "Challenges of Functional Analysis" by Vlasov V. A. Konovalova and Kurochkina is a unique educational resource that will become an indispensable assistant for students, graduate students and teachers engaged in mathematics and its applications. This work not only collects tasks, but also immerses the reader in the fascinating world of functional analysis, revealing its basic concepts and methods through practical examples and tasks. Functional analysis is one of the most interesting and relevant areas of mathematics, which finds application in a variety of fields: from physics to economics. The book offers readers not only theoretical foundations, but also practical tasks that will help to consolidate the knowledge gained. The authors, having rich experience in teaching and scientific activities, have created a material that will be useful both for self-study and as a supplement to the main courses. This book will be of interest primarily to undergraduate and graduate students who study mathematics, physics, computer science, and other exact sciences. It can also attract the attention of teachers who are looking for quality materials for their courses, as well as researchers working in the field of functional analysis and related disciplines. If you want to deepen your knowledge in this area or are just looking for interesting tasks for training, "Functional Analysis Tasks" will be an excellent choice. One of the key topics addressed in the book is the study of linear operators, their properties and applications. The authors raise questions regarding spectral theory, topological vectors, and functional spaces. Each task in the book is accompanied by detailed solutions and comments, which allows the reader not only to find the right answers, but also to understand how and why they were received. This makes the book especially valuable for those who seek not only to solve the problem, but also to better understand the material being studied. The style of the authors is distinguished by clarity and accessibility, which makes it easy to perceive even the most complex concepts. Vlasov V. A. and his colleagues are known for their textbooks and scientific articles, which have been recognized both in Russia and abroad. Their experience and deep understanding of the subject make it possible to create material that will be relevant and useful for many years. The book “Challenges to Functional Analysis” also touches on modern approaches and methods used in functional analysis, which makes it especially relevant in the light of recent advances in this field. Readers will be able to get acquainted with the latest research and their application, which will help them to be aware of the latest trends and discoveries. If you are looking for a high-quality functional analysis manual that combines theory and practice, then “Functional Analysis Tasks” will be a real find for you. This is not just a book with problems, but a whole world in which you can immerse yourself, studying and solving problems, developing your analytical abilities and mathematical thinking. Do not miss the opportunity to become part of this fascinating journey into the world of functional analysis!