"This paper describes the characteristics and performance of a novel spatial heterodyne spectrometer designed to measure the extremely faint [OII] 372.6 nm and 372.9 nm emission lines from the warm (10,000 K) ionized component of our Galaxy's interstellar medium. These [O II] lines are a principal coolant for this wide spread, photoionized gas and are a potential tracer of variations in the gas temperature resulting from unidentified interstellar heating processes that appear to be acting within the Galaxy. In the basic SHS system, Fizeau fringes of wavenumber-dependent spatial frequency are produced by a Michelson interferometer modified by replacing the return mirrors with diffraction gratings; these fringes are recorded on a position sensitive detector and Fourier transformed to recover the spectrum over a limited range centered at the Littrow wavenumber of the gratings. The system combines interferometric and field-widening gains in tandem to achieve 10,000-fold sensitivity gains compared to conventional grating instruments of similar size and resolving power. SHS systems also have relaxed flatness tolerances (20-50 times compared to Fabry-Perots) and do not require precision imaging to achieve diffraction-limited spectroscopic performance. Defects can largely be removed in data processing. Early results from our [OII] SHS system confirm the superb performance of the SHS technique for measurements of spatially extended faint emissions, including the first detection of [O II] emission lines extending out to 20 degrees from the Galactic equator ([OII] intensities ranged from tens of rayleighs near the Galactic plane to less than one rayleigh at high latitudes; the [OII] line profiles show structure indicating emission along the lines of sight from both the local interstellar gas and more distant gas in the Perseus spiral arm).--From the paper.