The book "Differential-difference equations" by the authors P. Bellman and K. Cook is an outstanding work that immerses the reader in the world of mathematical analysis and the theory of dynamical systems. This is not just a textbook, but a real find for students, graduate students and anyone interested in modern methods of solving complex equations. In it, the authors propose a deep and systematic approach to the study of differential and difference equations, which makes it an indispensable resource for future mathematicians and engineers. The book covers a wide range of topics, ranging from the foundations of the theory of differential equations to more complex concepts such as the stability of solutions and numerical methods. Bellman and Cook masterfully explain how to apply theoretical knowledge in practice, which is especially important for students seeking to apply mathematics to real-world problems. Each section of the book is imbued with clarity and logic, which allows readers to easily absorb the material and apply it in their research. This work will be especially useful for those interested in applied mathematics, physics and engineering. Graduate students and graduate students will find valuable ideas and methods in it that will help them in their scientific activities. In addition, the book will be of interest to teachers who are looking for a quality manual for their students. It can become the basis for courses in mathematical analysis, management theory and other related disciplines. The topics raised in Differential-Differential Equations cover not only mathematical aspects, but also philosophical ones. The authors discuss the importance of mathematical modeling in various fields of science and technology, emphasizing how differential equations can describe the dynamics of processes in nature and society. This makes the book relevant not only for mathematicians, but also for specialists in the natural and social sciences. Bellman and Cook's style is clear and accessible, which makes complex concepts understandable even for those who are just starting to study this topic. Their approach to learning is based on the principle of “from simple to complex”, which allows readers to gradually delve into the material. The authors also use many examples and tasks, which helps to consolidate theoretical knowledge in practice. R. Bellman is known for his work in the field of mathematical theory of control and optimization, and is the author of such well-known books as “Optimal control methods” and “Dynamic programming”. K. Cook, in turn, also has a significant contribution to the development of mathematical analysis and control theory. Their joint work in Differential-difference equations is a logical continuation of their scientific activity and demonstrates their deep understanding of the subject. If you are looking for a book that will not only deepen your knowledge in the field of differential equations, but also inspire you to new research and discoveries, then Bellman and Cook’s “Differential-Difference Equations” is exactly what you need. This book will be your reliable companion in the world of mathematics, opening up new horizons and opportunities for you. Do not miss the opportunity to get acquainted with a work that combines theory and practice, making complex mathematical concepts available to everyone.