[en] Layer-dependent quasiparticle band structures of the newly emerged honeycomb C₃N are systematically studied using both density functional theory and GW methods. The calculated GW band gap for monolayer C₃N is about 1.5 eV. This moderate band gap may be ideal for future electronics applications. Our result is in marked contrast with a recent experimental report of 0.39 eV and calls for future experimental verifications. Interlayer chemical coupling effects on the electronic structure of C₃N are investigated using several bilayer models. The electronic structure of bilayer C₃N depends sensitively on the layer stacking pattern with the calculated quasiparticle band gap ranging from 0.87 to 1.35 eV. Finally, we illustrate the effects of interlayer chemical interaction and bulk dielectric screening on the electronic properties of C₃N. Depending on the specific bulk stacking, C₃N may be metallic or semiconducting with a narrow gap of about 0.6 eV, even though different bulk phases are essentially degenerate energetically. As a result, it may be challenging to prepare single-phase semiconducting bulk C₃N unless synthetic kinetics can somehow prefer or prohibit certain stacking patterns. This issue deserves further investigations. (paper)