Spin-polarized scanning tunneling spectroscopy is well suited to study the correlation between structural, electronic and magnetic properties with high spatial and energy resolution. This thesis reports on the first observation of magnetization curves of individual atoms by spin-polarized scanning tunneling spectroscopy (single-atom magnetization curves), which is used to investigate Co atoms adsorbed on Pt(111) and Fe atoms adsorbed on Cu(111). A systematic study of different Co nanostructures on Pt(111) reveals an inversion of the spin polarization in the vacuum above individual Co atoms with respect to larger Co nanostructures, as e.g., dimers and layers, which is attributed to the enhanced rotation symmetry of single atoms. This effect is believed to be general for single magnetic atoms adsorbed on surfaces. The magnetization of the isolated Co atoms is found to be switching at 0.3 K, which is as yet too rapid to observe, and hence they behave paramagnetically. Fitting to a quasiclassical paramagnetic model, the magnetic moment is deduced to have a mean value of 3.5 &muB with a wide spreading. Co atoms located close to Co nanowires are proven to be stabilized due to the Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling with the nanowires which is probably mediated by a surface resonance of Pt(111). As revealed by the investigation of Co pairs the RKKY coupling depends strongly on the distance and especially on the relative direction with respect to the substrate on the atomic scale, which is attributed to the non-spherical Fermi surface of the substrate. The measured pairwise RKKY coupling map is demonstrated to reliably predict the magnetism of more complex nanostructures built from a larger number of atoms. The same indirect exchange interaction between distant individual Co atoms forms a spatially inhomogeneous mean field, giving rise to the spreading in the magnetic moments. A spin polarization above the Pt(111) surface in the vicinity of the Co nanowires is detected and found to be exponentially decaying in lateral distance from the interface with a long decay length of 1 nm. The investigation of Fe atoms on Cu(111) also reveals paramagnetism with an out-of-plane easy axis and an RKKY mean field with a comparable strength as for Co adatoms on Pt(111).