Laser cooling of electron beams at linear colliders

A method of electron beam cooling is considered which can be used for linear colliders. The electron beam is cooled during collision with focused powerful laser pulse. The ultimate transverse emittances are much below those achievable by other methods. This method is especially useful for high energy gamma-gamma colliders. In this paper we review and analyse limitations in this method, also discuss a new method of obtaining very high laser powers required for the laser cooling, radiation conditions and finaly present a possible scheme for the laser cooling of electron beams.