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We describe the design, construction, and characterization of the Band 9 heterodyne receivers (600-720 GHz) for the Atacama Large Millimeter / submillimeter Array (ALMA). The ALMA Band 9 receiver units ("cartridges"), which are installed in the telescope's front end, have been designed to detect and down-convert two orthogonal linear polarization components of the light collected by the ALMA antennas. The light entering the front end is refocused with a compact arrangement of mirrors, which is fully contained within the cartridge. The arrangement contains a grid to separate the polarizations and two beam splitters to combine each resulting beam with a local oscillator signal. The combined beams are fed into independent double-sideband mixers, each with a corrugated feedhorn coupling the radiation by way of a waveguide with backshort cavity into an impedance-tuned SIS junction that performs the heterodyne down-conversion. Finally, the generated intermediate frequency signals are amplified by cryogenic and room-temperature HEMT amplifiers and exported to the telescope's back end for further processing and, finally, correlation. The receivers have been constructed and tested in the laboratory and they show excellent performance, complying with ALMA requirements. Performance statistics on all 73 Band 9 receivers are reported. On-sky characterization and tests of the performance of the Band 9 cartridges are presented using commissioning data.