[en] MIT's High Resolution X-ray Spectroscopy investigation on AXAF involves two complementary dispersive instruments, a Bragg Crystal Spectrometer (BCS) and a High Energy Transmission Grating Spectrometer (HETGS). The overall goal of the investigation is to study the physical conditions in celestial sources by means of detailed measurements of their X-ray spectra. High spectral resolution measurements can be used to perform diagnostics of emitting and absorbing matter, leading to knowledge of temperature, ionization state, elemental abundance, density and optical depth. The Bragg Crystal Spectrometer gives resolving powers of 200-2000 over the energy band 0.5-8 keV and resolving powers of 50-70 over 0.14-0.5 keV. The effective collecting areas in a typical scanning observation are 4-60 cm/sup 2/, and the minimum detectable line flux is 4-30 X 10/sup -6/ photons cm/sup -2/ s/sup -1/. The BCS will be located at the AXAF focal plane. The instrument consists of 10 curved diffractors each of which has a quasi-toroidal geometry, two types of imaging proportional counters optimized for low background (one sealed and one flow), an internal monitor counter that can be inserted into the beam to measure total source flux, a mechanical system that maintains Rowland circle geometry and an appropriate command and data system. The BCS is an upgraded and improved version of the Focal Plane Crystal Spectrometer flown on the Einstein Observatory. It will be used to measure the strengths of individual lines from both point and extended objects in order to apply plasma diagnostic techniques to the study of cosmic X-ray sources