  We present spectral analysis of the Crab Nebula obtained with the {\it
Chandra} X-ray observatory. The X-ray spectrum is characterized by a power-law
whose index varies across the nebula. The variation can be discussed in terms
of the particle injection from the pulsar in two different directions: the
equatorial plane containing the torus and the symmetry axis along the jet. In
the equatorial plane, spectra within the torus are the hardest, with photon
index $\alpha \approx 1.9$, and are almost independent of the surface
brightness. At the periphery of the torus, the spectrum gradually softens in
the outer, lower surface brightness regions, up to $\alpha \approx 3.0$. This
indicates that synchrotron losses become significant to X-ray emitting
particles at the outer boundary of the torus. We discuss the nature of the
torus, incorporating information from observations at other wavelengths.
Spectral variations are also seen within the southern jet. The core of the jet
is the hardest with $\alpha \approx$ 2.0, and the outer sheath surrounding the
core becomes softer with $\alpha$ up to 2.5 at the outermost part. Based on the
similarity between the spectra of the jet core and the torus, we suggest that
the electron spectra of the particles injected from the pulsar are also similar
in these two different directions. The brightness ratio between the near and
far sides of the torus can be explained by Doppler boosting and relativistic
aberration; however, the observed ratio cannot be derived from the standard
weakly magnetized pulsar wind model. We also found a site where an optical
filament comprised of supernova ejecta is absorbing the soft X-ray emission
($<$ 2 keV).
