This thesis describes the design, construction and operation of an intense source of polarized electrons suitable for application to most proposed scattering experiments. Polarized electrons are produced in a flowing helium afterglow apparatus by chemiionization reactions involving optically pumped helium 2 S metastables. These electrons are electrostatically extracted from the flow tube and formed into a beam. The electron spin polarization is measured by a unique "on-line" Mott scattering polarization analyzer designed and constructed as an integral source component. In this thesis, applications for a polarized electron beam are reviewed and a comparison of the best available sources is made. The operation of the optically pumped flowing helium afterglow source is described in detail and current and polarization performance characteristics are reported: .1 pA at 5% polarization; 1 juA at 45%; 5 juA at 3% and 1 JJA at 2%. Measurements of the beam emittance show it to be very low (2 mrad-cm at 4 eV). Significant advantages of this source are the ease of electron spin reversal or modulation without a change in beam trajectory and the novel "on-line" Mott detector which allows simultaneous polarization analysis and low energy beam use. Several proposed experiments are suggested with a report on progress to date.