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In this work, we present the CoESCA station for electron-electron coincidence spectroscopy from surfaces, built in a close collaboration between Uppsala University and Helmholtz-Zentrum Berlin at the BESSY II synchrotron facility in Berlin, Germany. We start with a detailed overview of previous work in the field of electron-electron coincidences, before we describe the CoESCA setup and its design parameters. The system is capable of recording shot-to-shot resolved 6D coincidence datasets, i.e. the kinetic energy and the two take off angles for both coincident electrons. The mathematics behind extracting and analysing these multi-dimensional coincidence datasets is introduced, with a focus on coincidence statistics, resulting in fundamental limits of the signal-to-noise ratio and its implications for acquisition times and the size of the raw data stream. The functionality of the CoESCA station is demonstrated for the example of Auger electron - photoelectron coincidences from silver surfaces for photoelectrons from the Ag 3d core levels and their corresponding MNN Auger electrons. The Auger spectra originating from the different core levels, 3d$_{3/2}$ and 3d$_{5/2}$ could be separated and further, the two-hole state energy distributions were determined for these Auger decay channels.