  We present spatially resolved X-ray spectroscopy of PSR B1951+32 and its
pulsar wind nebula (PWN) in supernova remnant (SNR) CTB 80 using a {\sl
Chandra} observation. The {\sl Chandra} X-ray map reveals clearly various
components of a ram-pressure confined PWN embedded in the SNR ejecta: a point
source representing the pulsar, X-ray emission from the bow shock, a luminous
X-ray tail, a 30$\arcsec$ diameter plateau whose northwestern part is absent,
and the outside more diffuse X-ray emission. The plateau is just surrounded by
the radio, [O III], [S II], and [N II] shells, and the outside diffuse emission
is mostly within the H${\alpha}$ shells. While the spectra of all the features
are well fitted with power law models, a power law plus blackbody model can fit
the spectrum of the pulsar significantly better than using a power law model
alone. Generally the spectra of these components obey the trend of steepening
from the inside to the outside. However, the edge of the plateau probably has a
harder spectrum than that of the central region of the plateau. The cause of
the apparent hard spectrum of the plateau edge is unclear, and we speculate
that it might be due to a shock between the PWN and the SNR ejecta. The
possible blackbody radiation component from the pulsar has a temperature of
0.13$\pm0.02$ keV and an equivalent emitting radius of 2.2$^{+1.4}_{-0.8}$ (d/2
kpc) km, and is thus probably from the hot spots on the pulsar. We also show in
this paper that the blackbody temperature of the entire surface of PSR B1951+32
is much lower than those predicted by the standard neutron star cooling models.
