Far-infrared observations provide crucial data for the investigation and characterisation of the properties of dusty material in the Interstellar Medium (ISM), since most of its energy is emitted between ~100 and 200 um. We present the first all-sky image from a sensitive all-sky survey using the Japanese AKARI satellite, in the wavelength range 50 -- 180 um. Covering >99% of the sky in four photometric bands with four filters centred at 65 um, 90 um, 140 um, and 160 um wavelengths, this achieved spatial resolutions from 1 to 2 arcmin and a detection limit of <10 MJy sr-1, with absolute and relative photometric accuracies of <20%. All-sky images of the Galactic dust continuum emission enable astronomers to map the large-scale distribution of the diffuse ISM cirrus, to study its thermal dust temperature, emissivity and column density, and to measure the interaction of the Galactic radiation field and embedded objects with the surrounding ISM. In addition to the point source population of stars, protostars, star-forming regions, and galaxies, the high Galactic latitude sky is shown to be covered with a diffuse filamentary-web of dusty emission that traces the potential sites of high latitude star formation. We show that the temperature of dust particles in thermal equilibrium with the ambient interstellar radiation field can be estimated by using 90 um, 140 um, and 160 um data. The FIR AKARI full-sky maps provide a rich new data set within which astronomers can investigate the distribution of interstellar matter throughout our Galaxy, and beyond.