  The Crab nebula was observed with the H.E.S.S. stereoscopic
Cherenkov-telescope array between October 2003 and January 2005 for a total of
22.9 hours (after data quality selection). Observations were made with three
operational telescopes in late 2003 and with the complete 4 telescope array in
January - February 2004 and October 2004 - January 2005. The observations are
discussed and used as an example to detail the flux and spectral analysis
procedures of H.E.S.S., and to evaluate the systematic uncertainties in
H.E.S.S. flux measurements. The flux and spectrum of gamma-rays from the source
are calculated on run-by-run and monthly time-scales, and a correction is
applied for long-term variations in the detector sensitivity. Comparisons of
the measured flux and spectrum over the observation period, along with the
results from a number of different analysis procedures are used to estimate
systematic uncertainties in the measurements. The energy spectrum is found to
follow a power law with an exponential cutoff, with photon index $\Gamma = 2.39
\pm 0.03\stat$ and cutoff energy $E_{c} = (14.3 \pm 2.1\stat) \textrm{TeV}$
between 440 GeV and 40 TeV. The observed integral flux above 1 TeV is $(2.26
\pm 0.08\stat) \times 10^{-11} cm^{-2} s^{-1}$. The estimated systematic error
on the flux measurement is estimated to be 20%, while the estimated systematic
error on the spectral slope is 0.1.
