  We present the first long-slit spectra of the Seyfert 2 galaxy NGC 1068
obtained by the Space Telescope Imaging Spectrograph (STIS); the spectra cover
the wavelength range 1150 - 10,270 Angstroms at a spatial resolution of 0.05 -
0.1 arcsec and a spectral resolving power of 1000. In this first paper, we
concentrate on the far-UV to near-IR continuum emission from the continuum
``hot spot'' and surrounding regions extending out to +/- 6 arcsec (+/-432 pc)
at a position angle of 202 degrees In addition to the broad emission lines
detected by spectropolarimetry, the hot spot shows the ``little blue bump'' in
the 2000 - 4000 Ang. range, which is due to Fe II and Balmer continuum
emission. The continuum shape of the hot spot is indistinguishable from that of
NGC 4151 and other Seyfert 1 galaxies. Thus, the hot spot is reflected emission
from the hidden nucleus, due to electron scattering (as opposed to
wavelength-dependent dust scattering). The hot spot is ~0.3 arcsec in extent
and accounts for 20% of the scattered light in the inner 500 pc. We are able to
deconvolve the extended continuum emission in this region into two components:
electron-scattered light from the hidden nucleus (which dominates in the UV)
and stellar light (which dominates in the optical and near-IR). The scattered
light is heavily concentrated towards the hot spot, is stronger in the
northeast, and is enhanced in regions of strong narrow-line emission. The
stellar component is more extended, concentrated southwest of the hot spot,
dominated by an old (> 2 x 10 Gyr) stellar population, and includes a nuclear
stellar cluster which is ~200 pc in extent.
