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Micro-X is a sounding-rocket experiment that will combine a transition edge sensor (TES) microcalorimeter array with an imaging mirror to obtain high-spectral-resolution images of astronomical X-ray sources. The instrument's resolution across the 0.3-2.5 keV band will be 2 eV. The first flight will target the region of the Bright Eastern Knot of the Puppis A supernova remnant and is slated for January 2011. The obtained high-resolution X-ray spectra will be used to ascertain the temperature and ionization state of the X-ray-emitting gas and to determine its velocity structure. The TES array is read out by a time-division superconducting quantum interference device (SQUID) multiplexing system. The detector front end assembly and the SQUID multiplexing circuit are cooled to the operating temperature of 50 mK with an adiabatic demagnetization refrigerator (ADR). The design of this refrigerator is tailored to the requirements of rocket flight. Stable operation of the TES array close to the ADR magnet will be achieved with a magnetic shielding system, which will be based on a combination of a bucking coil and high-permeability and superconducting shield materials to cancel out residual fields. We describe our progress in developing the Micro-X instrument.