  The Chevalley-Eilenberg differential calculus and differential operators over
N-graded commutative rings are constructed. This is a straightforward
generalization of the differential calculus over commutative rings, and it is
the most general case of the differential calculus over rings that is not the
non-commutative geometry. Since any N-graded ring possesses the associated
Z_2-graded structure, this also is the case of the graded differential calculus
over Grassmann algebras and the supergeometry and field theory on graded
manifolds.
