We describe the Navy Prototype Optical Interferometer (NPOI), a joint project of the Naval Research Laboratory (NRL) and the US Naval Observatory (USNO) in cooperation with Lowell Observatory. The NPOI has recently begun operations at the Lowell Observatory site near Flagstaff, Arizona, obtaining its first images, of a binary star, in 1996 May and June and its first limb-darkening observations during 1996 November to 1997 February. This paper gives an overview of the NPOI, including the characteristics of optical interferometry that affect its design.The NPOI includes subarrays for imaging and for astrometry. The imaging subarray consists of six moveable 50 cm siderostats feeding 12 cm apertures, with baseline lengths from 2.0 to 437 m. The astrometric subarray consists of four fixed 50 cm siderostats feeding 12 cm apertures (35 cm apertures to be installed in 1998), with baseline lengths from 19 m to 38 m. The shared back end covers 450-850 nm in 32 channels. The NPOI features vacuum feed and delay systems, active group-delay fringe tracking, and a high degree of automation. The astrometric subarray also includes an extensive site laser metrology system to measure the motions of the siderostats with respect to one another and to the bedrock. For imaging stellar surfaces, arrays with equal spacing between elements are superior to arrays that have been laid out to optimize (u, v) coverage and that therefore have unequal spacing. The imaging subarray of the NPOI provides a number of equally spaced configurations with linear scales at ratios of ~1.64. Unequally spaced configurations are available for a variety of other imaging programs. Coherence across either type of imaging configuration is maintained by ``phase bootstrapping'': the phases on the longest baselines, on which fringes may be too weak to track, are stabilized by tracking fringes on the shortest baselines. In principle, the four elements of the astrometric subarray provide enough independent baselines to solve for stellar positions and the array geometry simultaneously while observing each of 11 stars only once. The anticipated magnitude limit is 7 mag or better with 12 cm apertures and average seeing; with 35 cm apertures, we expect the limit to be one or more magnitudes fainter. The anticipated wide-angle astrometric precision of the NPOI is ~2 mas. The best angular resolution of the imaging subarray will be ~200 μas. Our experience with the Mark III interferometer suggests that we will be able to measure stellar diameters as small as 200 μas with 1% precision and binary star separations as small as ρ ~ 65 μas (for ∆m ~ 0 mag) or ρ ~ 200 μas (for ∆m ~ 3-4 mag). With its large bandwidth and phase bootstrapping, the imaging subarray should be able to make images >~10 resolution elements across the disks of nearby late-type stars.