The quasar J513+0352 was observed on four different nights in service mode, on 15-16 Apr 2015 and 14-15 May 2015 under ESO program ID 095.A-0224(A) with the multi-wavelength, medium resolution spectrograph X-shooter mounted at the Cassegrain focus of the Very Large Telescope UT2.There are three tables included. The first table is the journal of observations including the observing date, slit widths, exposure time, seeing, airmass and position angle. The three different values for slit widths and exposure times correspond to the UVB, VIS and NIR arms, respectively. The exposure time for NIR data is sub-divided into 3 integrations (NDIT). Here, 'Seeing' refers to the "delivered seeing corrected by airmass" in the VIS Band and the value of 'Airmass' is recorded at start of exposure. The last column gives the position angle at the start of the observations. Table 2 contains column density details of the individual measurements of rotational levels of H2 with errorbars. Table 3 gives the column density of each metal component, HI and H2, and the corresponding X/H and X/Zn where 'X' refers to individual species of metals. (5 data files).