Details of the design, fabrication, ground and flight calibration of the High Energy Transmission Grating, HETG, on the Chandra X-ray Observatory are presented after five years of flight experience. Specifics include the theory of phased transmission gratings as applied to the HETG, the Rowland design of the spectrometer, details of the grating fabrication techniques, and the results of ground testing and calibration of the HETG. For nearly six years the HETG has operated essentially as designed, although it has presented some subtle flight calibration effects.