  Generalizing differential geometry of smooth vector bundles formulated in
algebraic terms of the ring of smooth functions, its derivations and the Koszul
connection, one can define differential operators, differential calculus and
connections on modules over arbitrary commutative, graded commutative and
noncommutative rings. For instance, this is the case of quantum theory, SUSY
theory and noncommutative geometry, respectively. The relevant material on this
subject is summarized.
