  We perform a cosmic shear analysis of the COMBO-17 survey -- a unique dataset
with shear quality R-band imaging and accurate photometric redshift estimates
(dz=0.05) for ~90% of galaxies to R=24.0. We undertake a full maximum
likelihood analysis to measure the weak lensing power spectra, Cl^kk, Cl^bb &
Cl^kb from l=400 to l=10^4. We find a strong measurement of the convergence
power over five fields. The b-field has a much lower significance, indicating
our data is free of major systematics, while the cross-correlation of k & b is
consistent with zero. We have also calculated the shear correlation functions
and variance over a range of scales between 0.5 and 20 arcmin. In addition, we
have used our results to measure cosmological parameters, constraining the
normalisation of the matter power spectrum to be sigma_8=(0.72 \pm
0.09)(Omega_m/0.3)^-0.49, where the errors quoted are 1-sigma due to the
intrinsic dispersion in galaxy ellipticities, cosmic and sampling variance. We
have significantly reduced the usual additional uncertainty in the median
redshift (z_m) of the survey by estimating z_m directly from the data. To
demonstrate the power of accurate redshift information, we have also measured
parameters from a shear analysis of only those galaxies with accurate
redshifts. In this case, we have eliminated the uncertainty in the redshift
distribution of sources and we show that the uncertainty in the resulting
parameter constraints are reduced by more than a factor of 2 compared to the
typical uncertainties found in cosmic shear surveys to date. Finally, we
combine our parameter measurements with constraints from the 2dFGRS and from
the CMB. With these additional constraints, we measure sigma_8=0.73 +0.05/-0.03
and Omega_m=0.27 +/- 0.02.
