The Near-Infrared Mapping Spectrometer (NIMS) is one of the science instruments in the Galileo mission, which will explore Jupiter and its satellites in the mid-1990's. The NIMS experiment will map geological units on the surfaces of the Jovian satellites and characterize their mineral content; and, for the atmosphere of Jupiter, investigate cloud properties and the spatial and temporal variability of molecular abundances. The optics are gold-coated reflective and consist of a telescope and a grating spectrometer. The balance of the instrument includes a 17-detector (silicon and indium antimonide) focal plane array, a tuning fork chopper, microprocessor-controlled electronics, and a passive radiative cooler. A wobbling secondary mirror in the telescope provides 20 pixels in one dimension of spatial scanning in a pushbroom mode, with 0.5 mr x 0.5 mr instantaneous field of view. The spectral range is 0.7 - 5.2μm; resolution is 0.025μm. NIMS is the first infrared experiment to combine both spatial and spectral mapping capability in one instrument.