[en] The authors describe a High Energy Transmission Grating Spectrometer that operates over the range 0.4-8 keV, gives resolving powers of 100-1000 and effective areas of 10-200 cm/sup 2/. The instrument, which is part of the MIT High Resolution X-ray Spectroscopy investigation, consists of a single array of grating facets of two types: medium energy gratings of 0.6 μm period, 0.5 μm thick silver mounted behind the outer three AXAF mirrors, and high energy gratings of 0.2 μm period, 1.0 μm thick gold mounted behind the inner three mirrors. The gratings are oriented so as to correct for coma and so that the medium and high energy spectra form a shallow ''X'' at the AXAF focal plane. The thicknesses and materials of the gratings are selected to give total first order diffraction efficiencies of up to 50%. The gratings are fabricated on thin polyimide films using techniques of X-ray lithography. They have been tested at energies of 5 to 15 keV. The minimum detectable line strength for point sources observed with the HETGS and a CCD detector is 1-10 X 10/sup -6/ photons cm/sup -2/ s/sup -1/. Likely targets include normal stars, binary X-ray sources, active galactic nuclei and quasars. The HETGS can also be used to give moderate resolution spectra of slightly extended sources and monochromatic images of sources with strong lines, such as supernova remnants in nearby galaxies