We present an overview and description of the e-MERGE Survey (e-MERLIN Galaxy Evolution Survey) Data Release 1 (DR1), a large program of high-resolution 1.5-GHz radio observations of the GOODS-N field comprising similar to 140 h of observations with enhanced-Multi-Element Remotely Linked Interferometer Network (e-MERLIN) and similar to 40 h with the Very Large Array (VLA). We combine the long baselines of e-MERLIN (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 (similar to 1.5 mu Jy beam(-1)), angular resolution (0.2-0.7 arcsec) and field-of-view (similar to 15x15 arcmin(2)) to detect and spatially resolve star-forming galaxies and active galactic nucleus (AGN) at z greater than or similar to 1. The goal of e-MERGE 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 an similar to 20-yr baseline and the development of newpoint spread function/primary beam models to seamlessly merge e-MERLIN and VLA data in the uv plane. We present early science results, including measurements of the luminosities and/or linear sizes of similar to 500 galaxies selected at 1.5 GHz. In combination with deep Hubble Space Telescope observations, we measure a mean radio-to-optical size ratio of r(e-MERGE)/r(HST) similar to 1.02 +/- 0.03, suggesting that in most high-redshift galaxies, the similar to GHz continuum emission traces the stellar light seen in optical imaging. This is the first in a series of papers that will explore the similar to kpc-scale radio properties of star-forming galaxies and AGN in the GOODS-N field observed by e-MERGE DR1.