We present a reanalysis of the Einstein Observatory high-resolution imager data, along with new radio and optical observations. These data are used to examine the morphology of the M87 jet, and together with infrared and UV data from the literature, are used to construct radio to x-ray spectra for the jet and nucleus. Two new features are isolated in the x-ray images, which we associate with the radio/optical knots B and D. The detailed morphology of the jet is nearly identical from the radio to x-ray bands. All the knots have a similar radio spectral index (S(v) proportional-to-nu-alpha) alpha-rr approximately 0.5. At higher frequencies the spectra steepen to optical/x-ray indices alpha-ox approximately 1.1 near the nucleus, and alpha-ox greater-than-or-similar-to 1.5 for the outer knots. Most of the steepening occurs in a sudden break between infrared and optical frequencies. The optical, UV, and x-ray data are consistent with a single power law connecting these frequencies; there is no evidence for the x-ray emission constituting a separate spectral component. Comparison of radio and optical images shows no evidence for spectral steepening in the interknot regions. We favor the synchrotron mechanism as the origin of the jet x-ray emission. Although it requires very high energy electrons with short lifetimes, it provides a natural explanation for alpha-oo approximately alpha-ox seen in several knots. Thermal models are untenable because they require high pressures and densities in the confining medium. Inverse Compton models require ad hoc distributions of low-energy electrons and/or infrared photons. The observed radio spectra are consistent with those expected for Fermi acceleration at strong nonrelativistic shocks. The shape of the high-frequency spectrum, however, is more difficult to explain; standard models which invoke synchrotron losses are unable to produce the observed values of alpha-oo and alpha-ox. Our optical data for the nucleus are consistent with the presence of an unresolved, blue continuum source. The resulting spectrum for the nucleus is similar to that of the jet, except at high radio frequencies.
