In the first pure postgrad seminar, Zoltan spoke about the persistent homology of a topological space. This, however, is just one example of a more general algebraic process of taking homology, which actually has very little to do with topology. I will describe this process and provide a motivation for it that comes from a first year undergraduate course on linear algebra. I will try to keep the talk as basic as possible, introducing only the concepts that are needed. After discussing homology, If I have enough time, I will give some applications to different areas of geometry.