Recent presentations of Information Geometry (IG), e.g. Amari and Nagaoka (2000), consider general statistical models and general sample spaces. However, the seminal discussion by Cenkov (transl. 1982) is based on finite sample spaces, as it is in Algebraic Statistics (AS). This talk will first review basic IG from the point of view of AS. In the second part, it discusses the issue of computation IG quantities and presents a few examples.