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DUNE is an international experiment dedicated to addressing some of the questions at the forefront of particle physics and astrophysics, including the mystifying preponderance of matter over antimatter in the early universe. The dual-site experiment will employ an intense neutrino beam focused on both a near detector and a cryogenic far detector. The DUNE far detector implements liquid argon time-projection chamber (LArTPC) technology, and combines many tens-of-kilotons of fiducial mass with sub-centimeter spatial resolution to collect neutrino events and image them with high precision. Given its size, this detector will be implemented as a set of up to four modules, each of which will require its own cryostat that will contain approximately 17.5 metric kilotons of ultra-pure liquid argon (LAr). The cryogenics infrastructure to support the detector modules includes systems to receive, transfer, store, purify, and maintain the LAr. This design report describes the cryostats and the cryogenics infrastructure required for the first two detector modules; this infrastructure is designed to support expansion to up to four far detector modules., Comment: 81 pages, 33 figures. Editor: A. Heavey