CompleteO(αs3)results fore+

We present the next-to-leading order (O(alpha_s^3)) perturbative QCDpredictions for e^+e^- annihilation into four jets. A previous calculationomitted the O(alpha_s^3) terms suppressed by one or more powers of 1/N_c^2,where N_c is the number of colors, and the `light-by-glue scattering'contributions. We find that all such terms are uniformly small, constitutingless than 10% of the correction. For the Durham clustering algorithm, theleading and next-to-leading logarithms in the limit of small jet resolutionparameter y_{cut} can be resummed. We match the resummed results to ourfixed-order calculation in order to improve the small y_{cut} prediction.Comment: Latex2e, 17 pages with 5 encapsulated figures. Note added regarding subsequent related work. To appear in Phys. Rev.