  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.
