The Extreme-Ultraviolet Imaging Spectrometer (EIS) is the first of a new generation of normal-incidence, two-optical-element spectroscopic instruments developed for space solar extreme-ultraviolet astronomy. The instrument is currently mounted on the Solar-B satellite for a planned launch in late 2006. The instrument observes in two spectral bands, 170-210 A and 250-290 A. The spectrograph geometry and grating prescription were optimized to obtain excellent imaging while still maintaining readily achievable physical and fabrication tolerances. A refined technique using low ruling density surrogate gratings and optical metrology was developed to align the instrument with visible light. Slit rasters of the solar surface are obtained by mechanically tilting the mirror. A slit exchange mechanism allows selection among four slits at the telescope focal plane. Each slit is precisely located at the focal plane. The spectrograph imaging performance was optically characterized in the laboratory. The resolution was measured using the Mg iii and Ne iii lines in the range of 171-200 A. The He ii line at 256 A and Ne iii lines were used in the range of 251-284 A. The measurements demonstrate an equivalent resolution of ~2 arc sec? on the solar surface, in good agreement with the predicted performance. We describe the EIS optics, mechanisms, and measured performance.