This thesis presents the first experimental results of a scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) investigation of rubrene at the supramolecular, molecular and submolecular level. Based on its semiconducting and fluorescent properties, this molecule is of particular interest in view of the emerging fields of molecular electronics and optoelectronics which could one day replace the conventional technology relying on semiconductors such as silicon and gallium arsenide. The goal is the substitution of these inorganic materials by cheap and flexible layers of semiconducting organic molecules for a new class of diodes and transistors, as well as the realization of electronic switches based on individual molecules. One fundamental approach is to take advantage of the molecular self-assembly behavior which results in the creation of well-ordered supramolecular structures. The investigations of the self-assembly of rubrene adsorbed on metal surfaces (Au(111), Au(100), Ag(111), and Ag(100)), which were carried out within the framework of this thesis, show a surprising diversity of supramolecular structures. Amongst other shapes, the molecules organize themselves into geometries of perfect hexagonal and pentagonal symmetry and create multifaceted patterns on the surface. A fascinating peculiarity consists in the spontaneous construction of nested structures which are built up by a hierarchical self-assembly of individual molecules into pentagonal supermolecules which form in a second step perfect supramolecular decagons. The geometric shape of rubrene is characterized by a structural asymmetry leading to the existence of two mirror imaged versions of the molecule which are not superimposable to each other, such as for instance our left and right hand or the helical DNA. The aspect of chirality is crucial for basic processes in living systems and calls for a fundamental understanding of the interaction mechanisms occurring between chiral molecules. The experiments on rubrene reveal that the intermolecular bonding differentiates between the two chiral types of the molecule (chiral recognition), yielding the self-organization into homochiral structures. These assemblies exhibit a geometry which is again chiral, demonstrating a propagation of chirality throughout the three stages of the supramolecular hierarchy. The semiconducting behavior of rubrene is furthermore probed by STS measurements detecting the energetic positions of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). The experimental data uncover that different adsorption conformations exhibit characteristic HOMO energies and reveal adsorption conformations of rubrene which preserve the intrinsic electronic structure of the free molecule. Furthermore, a switching of the molecular conformation and the electronic structure of one rubrene conformer is induced with the STM.