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abstract: 'In this paper, we present results of TeV $\gamma$–ray observations of the high synchrotron peaked BL Lac object 1ES 1218+304 (z=0.182) with the $TACTIC$ (TeV Atmospheric Cherenkov Telescope with Imaging Camera). The observations are primarily motivated by the unusually hard GeV-TeV spectrum of the source despite its relatively large redshift. The source is observed in the TeV energy range with the $TACTIC$ from March 1, 2013 to April 15, 2013 (MJD 56352–56397) for a total observation time of 39.62 h and no evidence of TeV $\gamma$–ray activity is found from the source. The corresponding 99$\%$ confidence level upper limit on the integral flux above a threshold energy of 1.1 TeV is estimated to be 3.41 $\times10^{-12}$ photons cm$^{-2}$ s$^{-1}$ (i.e $<23\%$ Crab Nebula flux) assuming a power law differential energy spectrum with photon index 3.0, as previously observed by the $MAGIC$ and $VERITAS$ telescopes. For the study of multi-wavelength emission from the source, we use nearly simultaneous optical, UV and and X–ray data collected by the UVOT and XRT instruments on board the *Swift* satellite and high energy $\gamma$–ray data collected by the Large Area Telescope on board the *Fermi* satellite. We also use radio data at 15 