We present high spatial resolution observations of the mid-infrared core of the dusty symbiotic system HM Sge obtained with the Very Large Telescope Interferometer (VLTI) of ESO's Paranal Observatory and MIDI, the MID-infrared Interferometric recombiner. MIDI combines the light of two telescopes and provides spectrally resolved visibilities in the N band atmospheric window. The observations of HM Sge were conducted with the VLT Unit Telescopes (UTs) UT2, UT3 and UT4, providing projected baselines in the range of 32-59 meters oriented from PA=42deg to 105deg and the Auxiliary Telescopes (ATs) E0 and G0, providing projected baselines in the range of 13.5-16 meters oriented around PA=75deg. The UTs observations were made during the nights of July 23-24th 2005, May 17th 2006 and June 11th 2006. The ATs observations were made during the nights of May 27th 2006 and June 16th 2006. All the observations were made under good atmospheric conditions (Mean[seeing]~1.01") with the worst seeing (~1.75") during the night of July 23th 2005. The files includes all visibility and differential phase data recorded from these observations as well as all the characteristics concerning the observations. The log of the observations is shown in Table 1 of the paper (table1.dat).