Publisher Summary This chapter focuses on the mathematical models for controlling the inventory of a single product. Models with constant demand rates, models with deterministic time-varying demand, periodic review stochastic demand models; and continuous review stochastic demand models have been discussed. Various applications of inventory theory in industry have been presented. In models with constant demand rates, a class of models that is based on the simplest demand assumption—that is, demand is deterministic and stationary—has been discussed. The chapter presents an overview of the major developments and results for single product inventory management. The majority of research in inventory has been focused on stochastic demand models. Because of their importance, one will consider separately discrete time and continuous time cases. When the inventory system is monitored on a continuous time basis, the analysis of such system requires the specification of the demand process to the system.