  A constructive approach to differential calculus on quantum principal bundles
is presented. The calculus on the bundle is built in an intrinsic manner,
starting from given graded (differential) *-algebras representing horizontal
forms on the bundle and differential forms on the base manifold, together with
a family of antiderivations acting on horizontal forms, playing the role of
covariant derivatives of regular connections. In this conceptual framework, a
natural differential calculus on the structure quantum group is described.
