The focus of this project has been devoted to the physics of low-dimensional systems in the range from 1D to 2D. For the experimental realization, epitaxial submonolayer coverages of metal atoms in ordered reconstructions on semiconductor surfaces have been used. Such model systems allow to tune the electronic properties by means of the atomic architecture, i.e., by choice of adatom and substrate as well as coverage or geometric phase. This enables systematic studies of prototypical many-body and interaction phenomena. In this project, we have specifically addressed the role of strong electronic correlations, including the concomitant occurence of magnetic ordering and strong spin-orbit coupling. Key model systems for this rich physics are 2D triangular (and hence frustrated) lattices as well as self-organized atomic nanowires. In this project we have studied the microscopic electronic structure of a number of such adatom systems locally in real space by scanning tunnel- ing microscopy/spectroscopy (STM/STS), and by measuring the single-particle excitation spectra by angle-resolved photoelectron spectroscopy (ARPES). The experimental results are closely accompa- nied by collaboration with theory. We have encountered a number of phenomena, such as spin order in atomic chains, indications for coupling between wires and parity breaking, as well as Mott physics and charge ordering in 2D systems.