The Extreme-ultraviolet Imaging Spectrometer combines, for the first time, high spectral, spatial and temporal resolution in a satellite based, solar extreme ultraviolet instrument. The instrument optical design consists of a multilayer-coated off- axis paraboloid mirror telescope followed by a toroidal grating spectrometer. The instrument includes thin film aluminum filters to reject longer wavelength solar radiation and employs CCD detectors at the focal plane. The telescope mirror is articulated to allow sampling of a large fraction of the solar surface from a single spacecraft pointing position. Monochromatic images are obtained either by rastering the solar image across the narrow entrance slit or by using a wide slit or slot in place of the slit. Monochromatic images of the region centered on the slot are obtained in a single exposure. Half of each optic is coated to maximize reflectance at 195 angstrom; the other half is coated to maximize reflectance at 270 angstrom. The two EUV wavelength bands were selected to optimize spectroscopic plasma diagnostic capabilities. Particular care was taken to choose wavelength ranges with relatively bright emission lines to obtain precision line of sight and turbulent bulk plasma velocity measurements from observed line profiles. The EIS spectral range contains emission lines formed over a temperature range from approximately 105 - 107 K. The wavelength coverage also includes several density sensitive emission line pairs. These line pairs provide spatial resolution independent density diagnostics at nominal coronal temperatures and densities. Each wavelength band is imaged onto a separate CCD detector. The main EIS instrument characteristics are: wavelength bands -- 180 - 204 angstrom and 250 - 290 angstrom; spectral resolution -- 0.0223 angstrom/pixel (23 - 34 km/second-pixel); slit dimensions -- 4 slits: 1 X 1024 arc- seconds and 50 X 1024 arc-seconds with two positions unspecified as of this writing; fine raster range -- >6 arc-minutes on the sun; coarse raster range -- > 1600 arc- seconds on the sun; largest spatial field of view in a single exposure -- 50 X 1024 arc-seconds; nominal time resolution for active region velocity studies -- 3.4s. The Solar-B satellite is scheduled for launch in August 2005 into a nominal 600 km sun-synchronous orbit.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.