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This is the first of a series of papers based on sensitive 610 MHzobservations of the ELAIS N1 field using the Giant Metrewave Radio Telescope.We describe the observations, processing and source catalogue extraction from adeep image with area of 1.86\,deg$^{2}$ and minimum noise of$\sim$7.1\,$\mu$Jy/beam. We compile a catalogue of 4290 sources with fluxdensities in the range 28.9\,$\mu$Jy - 0.503\,Jy, and derive theEuclidean-normalized differential source counts for sources with flux densitiesbrighter than $\rm{35.5\,\mu\,Jy}$. Our counts show a flattening at 610 MHzflux densities below 1 mJy. Below the break the counts are higher than previousobservations at this frequency, but generally consistent with recent models ofthe low-frequency source population. The radio catalogue is cross-matchedagainst multi-wavelength data leading to identifications for 92\% and reliableredshifts for 72\% of our sample, with 19\% of the redshifts based onspectroscopy. For the sources with redshifts we use radio and X-ray luminosity,optical spectroscopy and mid-infrared colours to search for evidence of thepresence of an Active Galactic Nucleus (AGN). We compare our identifications topredictions of the flux density distributions of star forming galaxies (SFGs)and AGN, and find a good agreement assuming the majority of the sources withoutredshifts are SFGs. We derive spectral index distributions for a sub-sample.The majority of the sources are steep spectra, with a median spectral indexthat steepens with frequency;$\mathrm{\alpha^{325}_{610}\,=\,-0.80\,\pm\,0.29}$,$\mathrm{\alpha^{610}_{1400}\,=\,-0.83\,\pm\,0.31}$ and$\mathrm{\alpha^{610}_{5000}\,=\,-1.12\,\pm\,0.15}$.

Deep GMRT 610 MHz Observations of the ELAIS N1 Field : Catalogue and Source Counts