The book "Convex Functions and Spaces of Orlich", written by outstanding scientists M. A. Redwood and me. B. Ruticki, is a deep and comprehensive study in the field of functional analysis that will be of interest to both professional mathematicians and students seeking to deepen their knowledge in this complex but fascinating field. In this book, the authors explore the concept of the convex functions and spaces of Orlich, which play a key role in modern analysis. Convex functions are known to have many interesting properties, and their study opens new horizons in various areas of mathematics, including optimization, game theory, and economics. Orlich spaces, in turn, are a generalization of classical Lebesgue spaces, which makes them especially relevant in the context of functional analysis and integration theory. The book begins with the basics, which makes it accessible to readers who do not have in-depth knowledge in this area. The authors consistently introduce the reader to the world of convex functions, explaining their properties and application. With each section, the reader plunges deeper into the topic, studying more complex concepts and theorems. This allows us not only to understand the theoretical foundations, but also to see how they are applied in practice. Who can like this book? First of all, it will be of interest to students and graduate students of mathematical faculties who study functional analysis, optimization theory and related disciplines . It will also be useful to practicing mathematicians working in the field of data analysis, probability theory and statistics. In addition, the book can attract the attention of researchers involved in the applied aspects of mathematics, who are looking for new approaches and methods for solving complex problems. The topics raised in the book cover a wide range of issues related to bulge, convex functions, and their properties. The authors elaborate on various aspects, such as the properties of convex functions, their application in optimization, and the role in game theory. The book also discusses the spaces of Orlich, their structure and application in real-world problems. This makes the book not only theoretically rich, but also practically useful. The style of the authors is distinguished by clarity and logical presentation, which allows the reader to easily assimilate complex concepts. Krasnoselsky and Rutitsky are known for their ability to explain even the most difficult topics in accessible language, which makes their work attractive to a wide audience. In addition, their previous publications, such as Functional Analysis and Optimization Methods, have already gained recognition among professionals and students, which adds additional value to their new book. “Convex Functions and Spaces of Orlich” is not just a textbook, but a real find for anyone who wants to deepen their knowledge in the field of functional analysis. The book will become a reliable companion for those who seek to understand complex mathematical concepts and apply them in their practice. Thanks to the accessible style of presentation and in-depth analysis of topics, it will be of interest to both beginners and experienced researchers. If you are looking for literature on functional analysis, optimization theory, or just want to expand your horizons in mathematics, this book will be an excellent choice. Do not miss the opportunity to immerse yourself in the world of convex functions and spaces of Orlich with the help of masters of your craft M. A. Krasnoselsky and I . B. Rutitsky .