This book introduces the mathematical theory of multistage decision processes using a functional equation approach to discover optimum policies. Written by Richard E. Bellman, a pioneer in the field, the text presents a series of methods, uniqueness and existence theorems, and examples for solving relevant equations. It delves into topics such as the optimal inventory equation, bottleneck problems in multistage production, a new formalism in the calculus of variation, strategies in multistage games, and Markovian decision processes.

This foundational text is regarded as a seminal work in the field of dynamic programming. Its rigorous approach and comprehensive coverage of multistage decision processes have made it a valuable resource for mathematicians, operations researchers, and computer scientists. The inclusion of problem sets, noted by Eric V. Denardo, further enhances its utility for both learning and research.