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The text, designed for students in Engineering Management or Industrial Engineering degree programs, brings together the mathematical models that underlie the basis of inventory management, a fundamental aspect in the context of production systems. The text aims to provide students with the following skills: - to know the assumptions to which the different models underlie, in order to be able to assess whether they can be applied to the practical case and, in the case of incomplete applicability, to acquire through experience the order of magnitude of the error being made; - to understand the logic by which the models were developed, in order to know how to adapt them to the many cases that arise in reality; - to know how to apply the models numerically, that is, how to use the computational tools and procedures necessary to obtain the quantitative results of interest. To this end, the text describes all the mathematical steps and demonstrations necessary for the development of each model, to which are added numerical examples of the model's application.