The Pierre Auger Observatory has begun a major Upgrade of its already impressive capabilities, with an emphasis on improved mass composition determination using the surface detectors of the Observatory. Known as AugerPrime, the upgrade will include new 4 m$^2$ plastic scintillator detectors on top of all 1660 water-Cherenkov detectors, updated and more flexible surface detector electronics, a large array of buried muon detectors, and an extended duty cycle for operations of the fluorescence detectors. This Preliminary Design Report was produced by the Collaboration in April 2015 as an internal document and information for funding agencies. It outlines the scientific and technical case for AugerPrime. We now release it to the public via the arXiv server. We invite you to review the large number of fundamental results already achieved by the Observatory and our plans for the future.