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Using density-functional and many-body perturbation theory, we study the electronic, optical, and excitonic properties of indium nitride as single monolayer and bilayer in comparison with the bulk phase. We investigate the stable geometry for the monolayer, the graphenelike unbuckled honeycomb structure, and for the bilayer the AA' stacking geometry. We demonstrate that the quasiparticle and optical gaps, going from bulk to two-dimensional systems, open dramatically due to strong quantum confinement and reduced screening. Large excitonic effects, which survive at room temperature, are predicted. Our results suggest that low-dimensional InN is a promising material for optoelectronic devices in the visible to near-infrared spectral ranges varying with the number of atomic layers and light propagation.