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Hyperons serve as powerful probes for investigating various aspects of quantum chromodynamics (QCD). As part of the FAIR Phase-0 program, the HADES (High-Acceptance Di-Electron Spectrometer) at GSI collected high-statistics proton-proton data using a proton beam with a kinetic energy of 4.5 GeV. The beam energy enables the production of hyperons close to threshold, facilitating studies of hyperon-hyperon interactions and searches for intermediate resonances. Currently, the ΛΛ reaction is being analyzed to extract crucial information on hyperon interactions, which is expected to be essential to understand the interiors of neutron stars. Furthermore, the first-time measurements of the Dalitz decay of the Σ0 will provide insights into transition form factors and thereby the electromagnetic structure of the Σ0. The study of Ξ- production in proton-proton collisions is valuable to address the observed excess yields observed in Ar+KCl and p+Nb reactions at HADES. This talk will highlight the ongoing hyperon physics analyses at HADES within the FAIR Phase-0 program and present selected results.