The book “Geometry of Jet Spaces and Its Applications to the Theory of Symmetry and the Laws of Conservation of Nonlinear Differential Equations” by Alexander Mikhailovich Vinogradov is a unique work. which opens to the reader the exciting world of mathematical theory and its practical applications Vinogradov, a well-known Russian mathematician and one of the founders of modern geometry, offers an in-depth analysis and systematization of knowledge about jets - mathematical objects that play a key role in the study of nonlinear differential equations. This book will be of interest to both specialists and those who are just beginning their journey in the study of mathematical disciplines. Students, graduate students and teachers working in the fields of mathematics, physics and engineering will find in it useful ideas and methods that will help them in research and practical activities . The book can also attract the attention of researchers engaged in symmetry theory and conservation laws, since Vinogradov considers these topics in terms of geometry and differential structure. The main theme of the book is the study of the spaces of jets, which are a generalization of classical concepts in mathematics. Grapes demonstrate how these spaces can be used to analyze the symmetries of nonlinear differential equations, which in turn leads to the detection of conservation laws. These laws are of great importance in physics because they describe the conservation of energy, momentum, and other important quantities in various systems. Vinogradov masterfully connects abstract mathematical concepts with real physical phenomena, which makes his work especially valuable for practitioners. The author's style is distinguished by clarity and logical presentation, which allows the reader to easily assimilate complex mathematical ideas. Vinogradov not only shares his knowledge, but also inspires further research in mathematics and physics. His previous works, such as Methods of Geometry and their Applications and Symmetry and Conservation Laws, have already established themselves as important sources for the study of these topics. In this book, he continues to develop his ideas, offering new approaches and methods. Readers interested in mathematics, physics, as well as methods for solving complex equations will find in the Geometry of Jet Spaces not only theoretical foundations, but also practical examples that will help them better understand how to apply this knowledge in real life. The book will also be useful for those who want to deepen their knowledge in the field of differential equations and their applications in various scientific disciplines. Grapes raise important topics such as the relationship between symmetry and conservation laws, and the role of geometry in understanding complex mathematical structures. These questions are relevant not only for mathematics, but also for physics, engineering and other scientific fields, which makes the book a universal source of knowledge. Thus, the “Geometry of Jet Spaces and Its Applications to the Theory of Symmetry and the Laws of Conservation of Nonlinear Differential Equations” is not just a textbook, but a real encyclopedia of ideas and methods that can change the approach to the study of nonlinear systems. This book will become an indispensable assistant for all who seek to understand complex mathematical and physical phenomena, and will inspire new discoveries in the world of science.