  We consider a simple and natural coboundary operator, on the Lie algebra
valued differential forms on a manifold, which in the abelian case reduces to
usual exterior derivative of such forms. Using the corresponding de Rham
cohomology Lie superalgebra H*(M,G) we obtain numerical smooth invariants--as
opposed to homotopy invariants--for manifolds. The corresponding Hodge theory
yields finiteness of nonabelian Betti numbers. A genralized Poincar\'{e} lemma,
along with a Poincar\'{e} duality, a Mayer-Vietoris, and a particularly
empowered Bockstein makes our cohomology computable. Bockstein also allows us
to relate (nonabelian) diffeomorphism invariants to (abelian) homotopy
invariants.
