  Using hydrogen and deuterium targets, Compton scattering by the proton and
neutron have been studied at the tagged photon beam of the MAMI (Mainz)
accelerator using different experimental setups. The theoretical tools for the
analysis of the experimental data have been investigated, as there are the
nonsubtracted dispersion theory and the theory of quasi-free reactions on the
proton and neutron bound in the deuteron. Experimental Compton scattering data
are understood in the first and second resonance region with good precision.
Precise electromagnetic polarizabilities and spin polarizabilities for the
proton and neutron have been determined.
