  Various aspects of the de Rham cohomology of Hopf algebras are discussed. In
particular, it is shown that the de Rham cohomology of an algebra with the
differentiable coaction of a cosemisimple Hopf algebra with trivial 0-th
cohomology group, reduces to the de Rham cohomology of (co)invariant forms.
Spectral sequences are discussed and the van Est spectral sequence for Hopf
algebras is introduced. A definition of
  Hopf-Lie algebra cohomology is also given.
