In this chapter we shall apply the theory of derived functors to the important special case where the cochain complex, sequence of abelian, n – cochain, cyclic, Rham cohomology. This will lead cohomology group Hn(X, G). In developing the theory we shall attempt to deduce as much as possible form general properties of derived functors. Thus or example we shall give a proof of the fact that Hn(X, G).