Abstract: Using the entire sample of 467 x 10(6) Y(4S) -> B (B) over bar decays collected with the BABAR detector at the PEP-II asymmetric-energy B factory at the SLAC National Accelerator Laboratory, we perform an analysis of B-+/- -> DK +/- decays, using decay modes in which the neutral D meson decays to either CP-eigenstates or non-CP-eigenstates. We measure the partial decay rate charge asymmetries for CP-even and CP-odd D final states to be A(CP+) = 0.25 +/- 0.06 +/- 0.02 and A(CP-) = 0.09 +/- 0.07 +/- 0.02, respectively, where the first error is the statistical and the second is the systematic uncertainty. The parameter A(CP+) is different from zero with a significance of 3.6 standard deviations, constituting evidence for direct CP violation. We also measure the ratios of the charged-averaged B partial decay rates in CP and non-CP decays, RCP+ 1.18 +/- 0.09 +/- 0.05 and RCP- = 1.07 +/- 0.08 +/- 0.04. We infer frequentist confidence intervals for the angle gamma of the unitarity triangle, for the strong phase difference delta(B), and for the amplitude ratio r(B), which are related to the B- -> DK- decay amplitude by r(B)e(i(delta B-gamma)) = A(B- -> (D) over bar K-0(-)) = A(B- -> (D) over bar K-0(-))/A(B- -> (DK-)-K-0). Including statistical and systematic uncertainties, we obtain 0: 24 < rB < 0: 45 ( 0: 06 < rB < 0: 51) and, modulo 180 degrees, 11.3 degrees < gamma < 22.7 degrees or 80.8 degrees < gamma < 99.2 degrees or 157.3 degrees < gamma < 168.7 degrees (7.0 degrees < gamma < 173.0 degrees) at the 68% ( 95%) confidence level.