  A microscopic theory for nuclear pairing is proposed through the generalized
density matrix formalism. The analytical equations are as simple as that of the
BCS theory, and could be solved within a similar computer time. The current
theory conserves the exact particle number, and is valid at arbitrary pairing
strength (including those below the BCS critical strength). These are the two
main advantages over the conventional BCS theory. The theory is also of
interests to other mesoscopic systems.
