A comprehensive bulk and surface investigation of high-quality In$_2$O$_3$(001) single crystals is reported. The transparent-yellow, cube-shaped single crystals were grown using the flux method. Inductively coupled plasma mass spectrometry (ICP-MS) reveals small residues of Pb, Mg, and Pt in the crystals. Four-point-probe measurements show a resistivity of 2.0 $pm$ 0.5 $times$ 10$^5$ {Omega} cm, which translates into a carrier concentration of $approx$10$^{12}$ cm$^{-3}$. The results from x-ray diffraction (XRD) measurements revise the lattice constant to 10.1150(5) {AA} from the previously accepted value of 10.117 {AA}. Scanning tunneling microscopy (STM) images of a reduced (sputtered/annealed) and oxidized (exposure to atomic oxygen at 300 {deg}C) surface show a step height of 5 {AA}, which indicates a preference for one type of surface termination. The surfaces stay flat without any evidence for macroscopic faceting under any of these preparation conditions. A combination of low-energy ion scattering (LEIS) and atomically resolved STM indicates an indium-terminated surface with small islands of 2.5 {AA} height under reducing conditions, with a surface structure corresponding to a strongly distorted indium lattice. Scanning tunneling spectroscopy (STS) reveals a pronounced surface state at the Fermi level ($E_F$). Photoelectron spectroscopy (PES) shows additional, deep-lying band gap states, which can be removed by exposure of the surface to atomic oxygen. Oxidation also results in a shoulder at the O 1s core level at a higher binding energy, possibly indicative of a surface peroxide species. A downward band bending of 0.4 eV is observed for the reduced surface, while the band bending of the oxidized surface is of the order of 0.1 eV or less.
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