  We derive in this paper expressions for the covariance matrix of the cosmic
shear two-point correlation functions which are readily applied to any survey
geometry. Furthermore, we consider the more special case of a simple survey
geometry which allows us to obtain approximations for the covariance matrix in
terms of integrals which are readily evaluated numerically. These results are
then used to study the covariance of the aperture mass dispersion which has
been employed earlier in quantitative cosmic shear analyses. We show that the
aperture mass dispersion, measured at two different angular scales, quickly
decorrelates with the ratio of the scales. Inverting the relation between the
shear two-point correlation functions and the power spectrum of the underlying
projected matter distribution, we construct estimators for the power spectrum
and for the band powers, and show that they yields accurate approximations; in
particular, the correlation between band powers at different wave numbers is
quite weak. The covariance matrix of the shear correlation function is then
used to investigate the expected accuracy of cosmological parameter estimates
from cosmic shear surveys. Depending on the use of prior information, e.g. from
CMB measurements, cosmic shear can yield very accurate determinations of
several cosmological parameters, in particular the normalization $\sigma_8$ of
the power spectrum of the matter distribution, the matter density parameter
$\Omega_{\rm m}$, and the shape parameter $\Gamma$.
