Dynamic programming is a newly emerging and intensively developing branch of mathematics that provides methods for solving important practical problems. It is about planning production or other processes when they are managed in a multi-stage way due to their complexity. Such tasks include, for example, the choice of the most suitable profile for the design of the railway track (broken into a number of sections), the choice of the best dimensions of the stages of a multi-stage rocket and many others. In this book, for the first time in the domestic literature, an attempt is made to publicly state the main ideas and methods of dynamic programming. The book is of interest to a wide range of science and production workers, as well as to all persons interested in the development of modern science.