We present maps of the IRAS large-scale 100-mu-m emission, after subtraction of a physical model for the zodiacal emission. There is a good detailed agreement with maps of the H I column density, assuming a normal gas-to-dust ratio, but several areas of very low dust column density can be identified. These may be of considerable importance for observations in the XUV band. Towards the Galactic Centre the 100 mu-m emissivity per hydrogen atom increases, due to the increased intensity of starlight, and towards the anticentre it declines as we look out into the outer part of the galactic disc. Maps of the 60-mu-m emission and the 100/60-mu-m flux ratio are presented. The contribution of zodiacal bands at beta = +/- 10-degrees can be clearly seen at 60-mu-m. Surprisingly, the bands are dimly traceable at 100-mu-m also, with a 60/100-mu-m flux ratio (after removal of the contribution of the cirrus) corresponding to a colour-temperature of 80 K. Maps of the 25 and 12-mu-m intensity, and of the 60/25-mu-m flux ratio, discriminate between narrow inner ((beta) < 5-degrees) bands of warmer dust, originating at the asteroid belts and not visible in the 100-mu-m maps, and cooler outer ((beta) = 8-15-degrees) bands, which presumably originate further out in the Solar System. The best-fitting blackbody curves to the 12-60-mu-m spectra of the bands have T = 250 K for the inner bands, and T = 170 K for the outer bands, which would place the latter at about twice the distance of the former for large dust grains. Alternatively the outer bands could be at 50 AU if they were composed of grains similar to interstellar grains. The excess radiation at 100-mu-m could then be understood as being due to an additional component of large grains at 40 K. A disc of dust between the orbit of Pluto and the Oort cloud has been postulated as a remnant of the solar nebula (Kuiper), as a perturber to Neptune's orbit (Whipple), and more recently as a source of short-period comets (Fernandez; Duncan, Quinn & Tremaine). A map of [I(100)-5I(60)] reveals the strong changes in dust temperature in the vicinity of molecular clouds, mostly near the galactic plane. Both regions of higher dust temperature, where new stars are forming, and cooler dust temperature, due to self-shielding of dust in cold, opaque molecular clouds from the interstellar radiation field, are seen. Away from the galactic and ecliptic planes the 60/100-mu-m flux ratio is fairly uniform. A prescription is given for calculating the visual extinction from the 100-mu-m intensity. A(v) is estimated to be 0.05 at the NGP and 0.08 at the SGP. The concepts of dust-free polar caps (Sandage), dust-free gas (Heiles, Stark & Kulkarni) and high polar extinction (de Vaucouleurs, de Vaucouleurs & Corwin) are not supported by the present study.