  The approach of Quillen to the cohomology of general algebraic systems is
based on simplicial methods, which are usually quite hard to deal with. The aim
of this work is to give the foundation of Shukla cohomology (of algebras over a
commutative ring) based on chain algebras. We also give an application to the
problem of strengthening additive track theories, which is based on the
comparison homomorphism between Shukla and Mac Lane cohomology theories.
