The (nu) over bar - e(-) elastic scattering cross section was measured with a CsI( Tl) scintillating crystal array having a total mass of 187 kg. The detector was exposed to an average reactor (nu) over bar flux of 6.4 x 10(12) cm(-2) s(-1) at the Kuo-Sheng Nuclear Power Station. The experimental design, conceptual merits, detector hardware, data analysis, and background understanding of the experiment are presented. Using 29882/7369 kg-days of Reactor ON/OFF data, the standard model (SM) electroweak interaction was probed at the squared 4-momentum transfer range of Q(2) similar to 3 x 10(-6) GeV2. The ratio of experimental to SM cross sections of xi = [1.08 +/- 0.21(stat) +/- 0.16(sys)] was measured. Constraints on the electroweak parameters (g(V); g(A)) were placed, corresponding to a weak mixing angle measurement of sin(W)(2 theta) = 0.251 +/- 0.031(stat) +/- 0.024(sys). Destructive interference in the SM (nu) over bar (e) - e process was verified. Bounds on anomalous neutrino electromagnetic properties were placed: neutrino magnetic moment at mu((nu) over bare) < 2. 2 +/- 10(-10) mu(B) and the neutrino charge radius at -2.1 X 10(-32) cm(2) < < r(nu e)(2)> < 3.3 X 10(-32) cm(2), both at 90% confidence level.