We present an overview and description of the eMERLIN Galaxy Evolution survey (eMERGE) Data Release 1 (DR1), a large program of high-resolution 1.5 GHz radio observations of the GOODS-N field comprising $sim140$ hours of observations with eMERLIN and $sim40$ hours with the Very Large Array (VLA). We combine the long baselines of eMERLIN (providing high angular resolution) with the relatively closely-packed antennas of the VLA (providing excellent surface brightness sensitivity) to produce a deep 1.5 GHz radio survey with the sensitivity ($sim 1.5mu$Jy beam$^{-1}$), angular resolution ($0.2$--$0.7$) and field-of-view ($sim15 times 15$) to detect and spatially resolve star-forming galaxies and AGN at $zgtrsim 1$. The goal of eMERGE is to provide new constraints on the deep, sub-arcsecond radio sky which will be surveyed by SKA1-mid. In this initial publication, we discuss our data analysis techniques, including steps taken to model in-beam source variability over a $sim20$ year baseline and the development of new point spread function/primary beam models to seamlessly merge eMERLIN and VLA data in the $uv$ plane. We present early science results, including measurements of the luminosities and/or linear sizes of $sim500$ galaxes selected at 1.5 GHz. In combination with deep Hubble Space Telescope observations, we measure a mean radio-to-optical size ratio of $r_{rm eMERGE}/r_{rm HST}sim1.02pm0.03$, suggesting that in most high-redshift galaxies, the $sim$GHz continuum emission traces the stellar light seen in optical imaging. This is the first in a series of papers which will explore the $sim$kpc-scale radio properties of star-forming galaxies and AGN in the GOODS-N field observed by eMERGE DR1.
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