Fluorescence microscopy is a widely used technique for imaging of biological structures due to its noninvasiveness although resolution of conventional fluorescence microscopes is limited to about 200-300 nm due to the diffraction limit of light. Super-resolution fluorescence microscopy offers an extension of the original method that allows optical imaging below the diffraction limit. In this thesis, a microscope for localization-based super-resolution fluorescence microscopy techniques such as Stochastic Optical Reconstruction Microscopy (STORM) or Photoactivated Localization Microscopy (PALM) was established. An epifluorescence microscope was built for this purpose that provides both widefield and Total Internal Reflection Fluorescence (TIRF) excitation modalities and focus was put on the special requirements of localization-based super-resolution methods. This included a high mechanical and optical stability realized by a compact design and implementation of a home-built perfect focus system. The setup was further designed to allow both two- and three-dimensional imaging. The work also included both the development of a setup control software and a software for the analysis of the required data. Different analysis methods and parameters were tested on simulated data before the performance of the microscope was demonstrated in two and three dimensions at appropriate test samples such as the cellular microtubule network. These experiments showed the capability of super-resolution microscopy to reveal underlying structures that cannot be resolved by conventional fluorescence microscopy. Resolutions could be achieved down to approximately 30 nm in the lateral and 115 nm in the axial dimension. Subsequently, the established method was applied to two biological systems. The first is a study of the budding of the human immunodeficiency virus type 1 (HIV-1) from the host cell. In this step of the viral reproduction cycle, the virus hijacks the cellular endosomal sorting complex required for transport (ESCRT) machinery to achieve membrane fission. ESCRT consists of the subcomplexes ESCRT-0, -I, -II and -III and additional related proteins, from which HIV-1 recruits certain components. The fission process is initiated by the HIV-1 Gag protein, which recruits the ESCRT-I protein Tsg101 and the ESCRT-related protein ALIX to the virus assembly site. Subsequently, ESCRT-III proteins CHMP4 and CHMP2 form transient lattices at the membrane, which are actively involved in membrane fission. However, the actual geometry of the ESCRT machinery assembling at the HIV-1 budding site that is driving the fission process is still not fully understood. Different models proposed either constriction of the budding neck by lattices surrounding the neck, by ESCRT structures within the neck or within the bud itself. A problematic aspect in previous studies was the usage of modified, tagged versions of the involved proteins for visualization. In this study, super-resolution microscopy was therefore applied to endogenous Tsg101, ALIX and CHMP2 isoform CHMP2A and to a version of CHMP4 isoform CHMP4B with a small HA-tag to elucidate the size and the distribution of the structure relative to the HIV-1 assembly sites. ESCRT structures colocalizing with HIV-1 exhibited closed, circular structures with an average size restricted to 45 and 60 nm in diameter. This size was significantly smaller than found for HIV-1 assembly sites and the constriction of the size, which was not observed for non-colocalizing ESCRT structures at the cell membrane, ruled out an external restriction model. Super-resolution imaging of ALIX often revealed an additional cloud-like structure of individual molecules surrounding the central clusters. This was attributed to ALIX molecules incorporated into the nascent HIV-1 Gag shell. Together with experiments that confirmed the non-physiological behavior of tagged Tsg101 and a relative orientation of ESCRT clusters towards the edge of