About the experiment (Information on E158 for a general audience can be found in the E158 public webpages.)     Over the past decade, experiments measuring weak neutral current interactions have taken the lead in the study of electroweak radiative corrections, providing the best indirect probes of new high energy physics. Experiments on the Z0 resonance have measured neutral current observables with spectacular precision, as evidenced by a precise indirect measurement of the mass of the top quark, which is in agreement with the direct measurement at the Tevatron.     At low Q2 on the other hand, tests of the electroweak theory in the weak neutral current sector are typically less sensitive by more than an order of magnitude. A comprehensive search for physics beyond the standard model is incomplete unless equally sensitive measurements are carried out both on and off the Z0 resonance.     A precision measurement of the left-right asymmetry (ALR) in Møller scattering (e-e--> e-e-, will use the 48 GeV polarized electron beam in End Station A (ESA) at SLAC scattering off unpolarized electrons in a liquid hydrogen target, corresponding to an average Q2 of 0.03 (GeV/c)2. The parity nonconserving piece of the electroweak interaction governing the Møller scattering process has never been measurement before.     The effective weak neutral current coupling governing low energy Møller scattering will be measured with a relative cumulative accuracy of 7% in a 5 month run, corresponding to a measurement of the weak mixing angle with the precision of ~ 0.0008. This would test the electroweak theory at the quantum loop level for Q2<< M2Z for the first time and provide unique sensitivity to new physics at the TeV scale. It allows the exploration of electron compositeness scale better than 10TeV, which achieves the same level of sensitivity as that accessed by LEP-II, the highest energy e+e- collider currently in operation.     The experiment would constitute the first time that a purely leptonic weak neutral current coupling is measured away from the Z0 pole with sufficient precision to access electroweak radiative corrections. Such a measurement would set a new standard for precision electroweak measurement at low Q2.