The Solar-B mission includes an Extreme-UV Imaging Spectrometer (EIS). It detects photons in the ranges 170-210 and 250-290 Å which include emission lines from several highly ionised species that exist at temperatures log T = 4.7, 5.6, 5.8, 5.9 and 6.0-7.3 K. In this paper, we will describe the design and operation of the instrument and present its performance parameters, e.g., spectral and spatial resolution and sensitivity. Preliminary results of recent calibration measurements will be described. Its role in the Solar-B mission will be illustrated with reference to several key science topics that the EIS is expected to address. The anticipated observing strategy for the first three months of the mission will be outlined.