The Far Ultraviolet Spectroscopic Explorer (FUSE), currently being fabricated and scheduled for a 1998 launch, is an astrophysics satellite designed to provide high spectral resolving power ((lambda) /(Delta) (lambda) equals 30,000) over the interval 910 - 1180 angstroms. It consists of four co- aligned, normal incidence mirrors that illuminate separate Rowland circle spectrograph channels equipped with holographic gratings and delay line microchannel plate detectors. The FUSE mirrors are rectangular, off-axis paraboloids with stringent reflectivity, imaging, lightweighting, and mechanical requirements. Two mirrors have Al + SiC coatings on Zerodur substrates, and the other two have Al + LiF coatings, also on Zerodur substrates. Important aspects of the optical and mechanical design are discussed, including the surface accuracy specifications at different spatial scales and the micropositioning actuators, which provide submicrometer focus and subarcsecond tip-and-tilt adjustment of the mirrors. Also discussed is the proposed design validation, including the predicted surface deformations induced in the mirrors when they are subjected to various gravitational and metrology mount conditions.