The physics program in Hall A at Jefferson Lab commenced in the summer of 1997 with a detailed investigation of the ^(16)O(e,e′p) reaction in quasielastic, constant (q,ω) kinematics at Q^2≈0.8(GeV/c)^2, q≈1GeV/c, and ω≈445MeV. Use of a self-calibrating, self-normalizing, thin-film waterfall target enabled a systematically rigorous measurement. Five-fold differential cross-section data for the removal of protons from the 1p-shell have been obtained for 0<p_miss<350MeV/c. Six-fold differential cross-section data for 0<E_miss<120MeV were obtained for 0<p_miss<340MeV/c. These results have been used to extract the ALT asymmetry and the R_L, R_T, R_LT, and R_(L+TT) effective response functions over a large range of E_miss and p_miss. Detailed comparisons of the 1p-shell data with Relativistic Distorted-Wave Impulse Approximation (RDWIA), Relativistic Optical-Model Eikonal Approximation (ROMEA), and Relativistic Multiple-Scattering Glauber Approximation (RMSGA) calculations indicate that two-body currents stemming from meson-exchange currents (MEC) and isobar currents (IC) are not needed to explain the data at this Q^2. Further, dynamical relativistic effects are strongly indicated by the observed structure in ALT at p_miss≈300MeV/c. For 25<E_miss<50MeV and p_miss≈50MeV/c, proton knockout from the 1s1/2-state dominates, and ROMEA calculations do an excellent job of explaining the data. However, as p_miss increases, the single-particle behavior of the reaction is increasingly hidden by more complicated processes, and for 280<p_miss<340MeV/c, ROMEA calculations together with two-body currents stemming from MEC and IC account for the shape and transverse nature of the data, but only about half the magnitude of the measured cross section. For 50<E_miss<120MeV and 145<p_miss<340MeV/c, (e,e′pN) calculations which include the contributions of central and tensor correlations (two-nucleon correlations) together with MEC and IC (two-nucleon currents) account for only about half of the measured cross section. The kinematic consistency of the 1p-shell normalization factors extracted from these data with respect to all available O16(e,e′p) data is also examined in detail. Finally, the Q^2-dependence of the normalization factors is discussed
