  We describe electron transport through small metallic grains with Coulomb
blockade effects beyond the perturbative regime. For this purpose we study the
real-time evolution of the reduced density matrix of the system. In the first
part of the paper we present a diagrammatic expansion for not too high junction
conductance, $h/4\pi^2e^2 R_t \lesssim 1$, in a basis of charge states. Quantum
fluctuations renormalize system parameters and lead to finite lifetime
broadening in the gate-voltage dependent differential conductance. We derive
analytic results for the spectral density and the conductance in the limit
where only two charge states play a role. In the second part of the paper we
consider junctions with large conductance, $h/4e^2 R_t \gtrsim 1$. In this case
contributions from all charge states, which broaden and overlap, become
important. We analyze the problem in a quasiclassical approximation. The two
complementary approaches cover the essential features of electron tunneling for
all parameters.
