The book “Eulerian Groups and Arithmetic of Geometric Progressions” by Vladimir Igorevich Arnold is a fascinating and in-depth study that opens the world of mathematical structures, their interconnections and applications in various fields of science to the reader. Arnold, known for his outstanding work in the field of mathematics, offers readers not just theoretical calculations, but also practical examples that make the material accessible and understandable. In this book, the author explores the concept of Euler groups that play a key role in number theory and algebra. Euler groups are mathematical structures with unique properties that allow solving complex problems related to arithmetic and geometry. Arnold skillfully combines rigorous mathematical evidence with intuitive explanations, making his work interesting for both professionals and students seeking to deepen their knowledge in the field. The book will be especially useful for those who are interested in mathematics at a deeper level. Students and graduate students studying mathematics, physics or engineering will find in it many useful ideas and methods that can be applied in their research. It can also attract the attention of teachers who are looking for new approaches to explain complex topics to their students. Mathematicians seeking to expand their horizons and understand how different mathematical concepts are interconnected will also appreciate this work. The topics raised in the book cover a wide range of issues, including the properties of numbers, the structure of arithmetic progressions, and their relationship to geometric concepts. Arnold not only explains how Euler's groups work, but also shows how they can be used to solve real-world problems. This makes the book not just a textbook, but a real guide to the world of mathematics, which inspires further research and discoveries. Arnold's style is clear and logical, which allows the reader to easily follow his thoughts. He skillfully uses real-life examples to illustrate complex concepts, making the material more lively and engaging. By reading this book, you not only immerse yourself in the world of abstract mathematics, but also begin to see how these ideas can be applied in everyday life. In addition to Euler's Group and the Arithmetic of Geometrical Progressions, Arnold is the author of many other well-known works, such as Ordinary Differential Equations and Geometry. His works often become classics, and this book is no exception. It represents an important contribution to mathematical literature and will be of interest to both professional mathematicians and those who are just beginning their journey in this fascinating science. If you are looking for a book that will help you understand complex mathematical concepts and teach you how to put them into practice, Euler Groups and Geometric Progression Arithmetic will be an excellent choice. This work will not only expand your knowledge, but also inspire new ideas and discoveries, opening up to you the limitless possibilities that mathematics offers.