A comprehensive study of single and double core ionization potentials of the aminophenol molecule is reported. The role of relaxation, correlation, relativistic, and basis set effects in these potentials is clarified. Special attention is paid to the isomer dependence of the single and double core ionization potentials. Some of them are also compared with the respective values of the phenol and aniline molecules. It is shown that the core level single ionization potentials of the para-, meta-, and ortho-aminophenol molecules differ only slightly from each other, rendering these structural isomers challenging to distinguish for conventional x-ray photoelectron spectroscopy. In contrast, the energy needed to remove two core electrons from different atoms depends noticeably on the mutual arrangement and even on the relative orientations of the hydroxyl and amine groups. Together with the electrostatic repulsion between the two core holes, relaxation effects accompanying double core ionization play a crucial role here. The pronounced sensitivity of the double ionization potentials, therefore, enables a spectroscopic characterization of the electronic structure of aminophenol isomers by means of x-ray two-photon photoelectron spectroscopy.