The book "Convex Functions and Spaces of Orlich", written by outstanding scientists M. A. Redwood and me. B. Ruticki, is a deep and fascinating study in the field of mathematical analysis and functional analysis. This publication will be of particular interest to those seeking to understand the complex concepts of convex functions and their applications in various fields of science and technology. The book focuses on convex functions that play a key role in optimization, game theory, and economics. The authors undertake the task not only to explain the basic concepts, but also to show how they can be used to solve real problems. The book examines the spaces of Orlich, an extensive class of functional spaces that summarize the known spaces of Lebesgue and Sobolev. This makes the work particularly valuable for researchers and practitioners working in the field of mathematical modeling and analysis. The book will be of interest to both undergraduate and graduate students, as well as specialists in mathematics, physics and engineering, who are looking for new approaches to solving complex problems. If you are passionate about mathematics and strive to expand your knowledge in the field of functional analysis, this publication will be a real find for you. It will help you not only to deepen your theoretical knowledge, but also to learn how to apply them in practice. Authors, M. A. Krasnoselsky and I . B. Rutitsky is known for his unique style of presentation, which combines the rigor of mathematical analysis with accessibility to a wide audience. Their work on functional analysis and operator theory has long won recognition in the scientific community. Krasnoselsky, for example, is the author of such well-known works as “Functional analysis” and “Linear operators in functional spaces”. These books may also be of interest to readers who are looking for a deeper understanding of functional spaces theory. The topics raised in Orlich's Convex Functions and Spaces cover a wide range of issues, including the properties of convex functions, their application in optimization theory, and their relationship to other areas of mathematics. The authors examine in detail various aspects, such as continuity, differentiation, and integrability, which allows the reader to gain a holistic view of the subject. The book also draws attention to the practical applications of the theory of convex functions in economics and social sciences. For example, convex functions are often used to model consumer preferences and analyze market mechanisms. This makes the work not only theoretically significant, but also practically useful for professionals working in these fields. Thus, “Convex Functions and Spaces of Orlich” is not just a textbook, but a real encyclopedia of knowledge for everyone who is interested in modern trends in mathematics. The book offers the reader the opportunity to immerse himself in the world of complex mathematical concepts, enriching his knowledge and expanding the horizons of understanding. If you are looking for literature that combines theory and practice, this publication will be an indispensable assistant for you on the way to mastering functional analysis and its applications. Do not miss the chance to discover new horizons in mathematics with this outstanding work!