  Large area lensing surveys are expected to make it possible to use cosmic
shear tomography as a tool to severely constrain cosmological parameters. To
this end, one typically relies on second order statistics such as the two -
point correlation fucntion and its Fourier counterpart, the power spectrum.
Moving a step forward, we wonder whether and to which extent higher order
stastistics can improve the lensing Figure of Merit (FoM). In this first paper
of a series, we investigate how second, third and fourth order lensing
convergence moments can be measured and use as probe of the underlying
cosmological model. We use simulated data and investigate the impact on moments
estimate of the map reconstruction procedure, the cosmic variance, and the
intrinsic ellipticity noise. We demonstrate that, under realistic assumptions,
it is indeed possible to use higher order moments as a further lensing probe.
