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 emph{Swift} satellite and high energy $gamma$--ray data collected by the Large Area Telescope on board the emph{Fermi} satellite. We also use radio data at 15 GHz from OVRO 40 m telescope in the same period. No significant increase of activity is detected from radio to TeV $gamma$--rays from 1ES1218+304 during the period from March 1, 2013 to April 15, 2013.
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