  We apply noncommutative geometry to a system of N parallel D-branes, which is
interpreted as a quantum space. The Dirac operator defining the quantum
differential calculus is identified to be the supercharge for strings
connecting D-branes. As a result of the calculus, Connes' Yang-Mills action
functional on the quantum space reproduces the dimensionally reduced U(N) super
Yang-Mills action as the low energy effective action for D-brane dynamics.
Several features that may look ad hoc in a noncommutative geometric
construction are shown to have very natural physical or geometric origin in the
D-brane picture in superstring theory.
