  We construct a particle-number(n)-resolved master equation (ME) approach
under the self-consistent Born approximation (SCBA) for quantum transport
through mesoscopic systems. The formulation is essentially non-Markovian and
incorporates the interlay of the multi-tunneling processes and many-body
correlations. The proposed n-SCBA-ME goes completely beyond the scope of the
Born-Markov master equation, being applicable to transport under small bias
voltage, in non-Markovian regime and with strong Coulomb correlations. For
steady state, it can recover not only the exact result of noninteracting
transport under arbitrary voltages, but also the challenging nonequilibrium
Kondo effect. Moreover, the n-SCBA-ME approach is efficient for the study of
shot noise.We demonstrate the application by a couple of representative
examples, including particularly the nonequilibrium Kondo system.
