When ideas for the SPS proton–antiproton collider firmed up, it was realized that the abundant production of antiprotons offered a further unique possibility: the deceleration and cooling would provide low-energy antiproton beams of unprecedented intensity and purity. A proposal was made to add a small facility for experiments with cooled antiproton beams in the energy range of 5 to 1200MeV. This was to become the Low-Energy Antiproton Ring, LEAR. Originally thought to only exist parasitically on the antiproton production for the SPS Collider, the project took on an ever-growing importance and, owing to its great successes, has even outlived the SPS Collider. It continues to this day in the simplified form of the Antiproton Decelerator, AD. Our paper describes the accelerator aspects of this venture.