Even very basic algebraic geometry provides a powerful set of tools to study discrete statistical models. In this chapter we provide some elementary introduction to polynomial algebra and algebraic and analytic geometry. This material is by no means complete, but may help to focus on the study of more specialized textbooks like Cox et al.  and Smith et al. . In addition, we provide a basic account of real algebraic geometry and tensor algebra. See the bibliographical notes at the end of this chapter for further references.