  We study the phase structure and Hall conductance quantization in weakly
coupled multi-layer electron systems in the integer quantum Hall regime. We
derive an effective field theory and perform a two-loop renormalization group
calculation. It is shown that (i) finite interlayer tunnelings (however small)
give rise to successive metallic and insulating phases and metal-insulator
transitions in the unitary universality class. (ii) The Hall conductivity is
not renormalized in the metallic phases in the 3D regime. (iii) The Hall
conductances are quantized in the insulating phases. In the bulk quantum Hall
phases, the effective field theory describes the transport on the surface.
