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In this thesis we study the electronic structure of different two-dimensional (2D) electron systems with angular resolved photoemission spectroscopy (ARPES). This technique is based on the photoelectric effect and directly probes the electronic structure of a system. By carefully analyzing the measured band structure with respect to peak position and line width we can determine the complex self-energy Σ that describes the renormalization of the electron's energy and the change in lifetime due to many-body interactions. The 2D electron systems investigated in this work are surface alloys on Ag(111), bismuth trimers on Si(111) and epitaxial graphene monolayers grown on SiC(0001). Surface alloys on Ag(111) are formed by depositing 1/3 of a monolayer of bismuth, lead or antimony (alloy atoms) on the clean silver surface. Although (Bi,Pb,Sb) and Ag atoms are immiscible in the bulk they form long-range ordered surface alloys, where every third Ag atom is replaced by an alloy atom. These systems as well as the Bi trimers on Si(111) show a spin splitting of the 2D band structure due to the Rashba-Bychkov (RB) effect. The RB model states that in a symmetry broken environment (such as the surface of a semi-infinite crystal) the spin-orbit interaction will lift the spin-degeneracy of the band structure. Such a spin-split band structure bares great potential for applications in the field of spintronics, e.g. in a Datta-Das spin field effect transistor. In the present work we investigate the origin of the observed giant spin splitting in surface alloys, especially the interplay between structural parameters and the atomic spin-orbit interaction. Furthermore, we will show that it is possible to transfer these concepts to a semiconducting substrate, which is better suited for spintronics applications. The third system under investigation — graphene — is an ideally two-dimensional crystal. It consists of a single layer of carbon atoms arranged in a honeycomb lattice, and its charge carriers are confined within a plane that is just one atom thick. These charge carriers behave like massless Dirac particles and possess extremely high carrier mobilities. This makes graphene a promising material system for high-speed electronic devices. In order to reach this ambitious goal one needs reliable methods for the large-scale production of high quality graphene films. Epitaxial growth on silicon carbide (0001) substrates is the method of choice in this case, as it offers the advantage of a precise thickness control and a semiconducting substrate at the same time. However, the presence of the substrate reduces the carrier mobility of graphene's charge carriers considerably. Therefore, it is necessary to decouple the graphene layer from the substrate after epitaxial growth. A second issue that needs to be addressed, are viable doping methods for graphene. As graphene's peculiar band structure results from a sensible interplay between electrons and crystal lattice it is not an option to replace single atoms of the graphene lattice by dopants as is common practice when doping silicon. In order to preserve its band structure, graphene is usually doped by adsorbing atoms or molecules on its surface. As graphene grown on SiC is n-doped due to charge transfer from the substrate, appropriate means for p-type doping are clearly required. In this thesis, we will present a new growth method for quasi free-standing graphene on SiC(0001) and viable means for p-type doping.