We present Space Telescope Imaging Spectrograph (STIS) spectral images of the HH 30 stellar jet taken through a wide slit over two epochs. The jet is unresolved spectrally, so the observations produce emission-line images for each line in the spectrum. This rich dataset shows how physical conditions in the jet vary with distance and time, produces precise proper motions of knots within the jet, resolves the jet width close to the star, and gives a spectrum of the reflected light from the disk over a large wavelength range at several positions. We introduce a new method for analyzing a set of line ratios based on minimizing a quadratic form between models and data. The method generates images of the density, temperature and ionization fraction computed using all the possible line ratios appropriately weighted. In HH 30, the density declines with distance from the source in a manner consistent with an expanding flow, and is larger by a factor of two along the axis of the jet than it is at the periphery. Ionization in the jet ranges from ~ 5% - 40%, and high ionization/excitation knots form at about 100 AU from the star and propagate outward with the flow. These high-excitation knots are not accompanied by corresponding increases in the density, so if formed by velocity variations the knots must have a strong internal magnetic pressure to smooth out density increases while lengthening recombination times.