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Based on first-principles calculations, the effects of the intrinsic defects and edge states on electronic structures and magnetic properties of AlN nanosheets (NSs) and nanoribbons (NRs) are investigated. In comparison to Al-defective AlN NS, N-defective systems can be easily achieved in experiments, and show a ferromagnetic (FM) property with Curie temperatures above room temperature. For quasi one-dimensional (1D) single-layer zigzag (ZZ) and armchair (AC) AlNNRs with and without edge atoms passivated by hydrogen, the bare and H-passivated AC and ZZNRs are found to be nonmagnetic (NM) semiconductors, whereas a FM character occurs in bare ZZNRs. We also find that the bandgap in H-passivated NRs decreases with the increase of the width of NRs, while bandgap in bare ACNRs increases with increasing the ribbon width. More interesting, in the case of multilayer ZZNRs, when the number of Al-N layers are even, they show NM semiconducting characters, while the odd-layer ZZNRs exhibit magnetic behaviors. Our predicted diverse and tunable electronic and magnetic properties endow AlN nanostructures potential applications in electronics and spintronics.