In this chapter, we start with the simplest epidemiological models and consider both infections that are strongly immunizing as well as those that do not give rise to immunity. In either case, the underlying philosophy is to assume individuals are either susceptible to infection, currently infectious, or recovered (previously infected and consequently immune). Although the progress between these classes could be presented as a verbal argument, to make quantitative predictions we must translate them into formal mathematical terms. This chapter presents the mathematical equations describing these models, together with the kinds of model analyses that have proved useful to epidemiologists. These approaches encompass both deterministic and probabilistic frameworks. The preliminary models will, of necessity, be somewhat primitive and ignore a number of well-known and important heterogeneities, such as differential susceptibility to infection, contact networks, variation in the immunological response, and transmissibility. Many of these complexities are addressed in subsequent chapters.