  The general features of the Moller scattering and its use as an electron
polarimeter are described and studied in view of the planned future high energy
e^+e^- linear colliders. In particular the study concentrates on the TESLA
collider which is envisaged to operate with longitudinal polarised beams at a
centre of mass energy of the order of 0.5 TeV with a luminosity of about L =
10^34 cm^-2 sec^-1.
