The goal of this talk is to give an introduction to the concept of Tate homology for non-experts. We will start out by explaining the basic concepts of projective resolution, complete resolution, and homotopy equivalence. With this tool set, we are then able to define the Tate homology and understand why it is well-defined. In the final part of the talk, we will relate the Tate homology to the group (co)homology and see how we can use this relation to efficiently compute the Tate homology in some situations.