  Quantum electrodynamics in a laser is formulated, in which the electron-laser
interaction is exactly considered, while the interaction of an electron and a
single photon is considered by perturbation. The formulation is applied to the
electron-laser collisions. The effect of coherence between photons in the laser
is therefore fully considered in these collisions. The possibility of
$\gamma-$ray laser generation by use of this kind of collision is discussed.
