I will give some constructions of homology and cohomology theories. The goal is to first motivate (co)homology, then give many different ways to compute and think about cohomology, and in the end reconcile all of these approaches with a very general theory. In terms of the general theory I will at least talk about Eilenberg-Steenrod axioms, derived functors, and the homotopical interpretation of cohomology. If I figure out a way to present it, I will talk about the general interpretation of cohomology in terms of the Hom set of an (\infty,1)-topos.