"The operator of the shift along the trajectories of differential equations" is a fascinating and deep work written by an outstanding mathematician and scientist Mikhail Alexandrovich Krasnoselsky. This book is not just a textbook, but a real encyclopedia devoted to one of the most interesting and complex topics in mathematics - differential equations and their applications. The author focuses on the shift operator, which plays a key role in the theory of differential equations. Krasnoselsky masterfully explains how this operator can be used to analyze and solve various problems related to dynamic systems. The reader immerses himself in a world of mathematical models that describe real-world processes, from mechanics to biology, and learns to put theoretical knowledge into practice. This book will be of interest to both students and professional mathematicians and physicists, as well as anyone who is fond of mathematical modeling and control theory. If you study mathematics at the level of higher education or work in the field of applied mathematics, then the “Movement Operator on the trajectories of differential equations” will become an indispensable source of knowledge for you. It is suitable for those who seek to deepen their knowledge in the field of differential equations and their practical applications, as well as for those who want to expand their horizons in mathematical analysis. The topics raised in the book cover a wide range of issues, such as the stability of solutions to differential equations, methods of numerical solution, and the relationship between theory and practice. Krasnoselsky not only outlines the theory, but also demonstrates how it can be used to solve real problems. This work stands out for its depth and thoroughness, which makes it worthy of the attention of not only specialists, but also lovers of mathematics. The author's style is clear and accessible, which allows the reader to easily assimilate complex concepts. Mikhail Alexandrovich Krasnoselsky is known for his other works, such as