Hi-GAL, the Herschel infrared Galactic Plane Survey: photometric maps and compact source catalogues. First data release for Inner Milky Way: +68{\deg}> l > -70{\deg}

(Abridged) We present the first public release of high-quality data products (DR1) from Hi-GAL, the {\em Herschel} infrared Galactic Plane Survey. Hi-GAL is the keystone of a suite of continuum Galactic Plane surveys from the near-IR to the radio, and covers five wavebands at 70, 160, 250, 350 and 500 micron, encompassing the peak of the spectral energy distribution of cold dust for 8 l > -70{\deg} in a |b|<1{\deg} latitude strip. Photometric maps have been produced with the ROMAGAL pipeline, that optimally capitalizes on the excellent sensitivity and stability of the bolometer arrays of the {\em Herschel} PACS and SPIRE photometric cameras, to deliver images of exquisite quality and dynamical range, absolutely calibrated with {\em Planck} and {\em IRAS}, and recovering extended emission at all wavelengths and all spatial scales. The compact source catalogues have been generated with the CuTEx algorithm, specifically developed to optimize source detection and extraction in the extreme conditions of intense and spatially varying background that are found in the Galactic Plane in the thermal infrared. Hi-GAL DR1 images will be accessible via a dedicated web-based image cutout service. The DR1 Compact Source Catalogues are delivered as single-band photometric lists containing, in addition to source position, peak and integrated flux and source sizes, a variety of parameters useful to assess the quality and reliability of the extracted sources, caveats and hints to help this assessment are provided. Flux completeness limits in all bands are determined from extensive synthetic source experiments and depend on the specific line of sight along the Galactic Plane. Hi-GAL DR1 catalogues contain 123210, 308509, 280685, 160972 and 85460 compact sources in the five bands, respectively.