| The Standard Model (SM) of particle physics successfully describes all of the observed interactions of the fundamental particles (with the exception of non-zero neutrino mass). Despite this enormous success, the SM is widely viewed as an incomplete theory. For example, the size of the asymmetry between matter and antimatter is not nearly large enough to account for the abundance of matter observed throughout the universe. It is thus believed that as-yet-unknown physical phenomena must exist that introduce new asymmetries between matter and antimatter. In this thesis, by studying decays that happen only rarely in the SM, we make measurements of asymmetries between matter and antimatter that are potentially sensitive to the existence of processes beyond the SM.;At the PEP-II asymmetric-energy B Factory at SLAC, electrons and positrons are collided at the Upsilon(4S) resonance to create pairs of B mesons. The BABAR detector is used to measure the subsequent decay products. Using 383 million Upsilon(4 S) → BB decays, we study the decay B0 → K +K-K 0. In the SM, this decay is dominated by loop amplitudes. Asymmetries between matter and antimatter (CP asymmetries) are extracted by measuring the time-dependence of the complex amplitudes describing the B 0 and B0 decays as functions of their kinematics. The interference between decays with and without the mixing of neutral B mesons allows for the measurement of the angle betaeff, which is a measure of CP violation. We also measure the direct CP asymmetry ACP.;Data samples reconstructed from three K0 modes ( K0S → pi+pi-, K0S → pi0pi0, and K0L ) are fit simultaneously. We find ACP = -0.015 +/- 0.077 +/- 0.053 and betaeff = 0.352 +/- 0.076 +/- 0.026 rad, corresponding to a CP violation significance of 4.8sigma. A second solution near pi/2 - beta eff is disfavored with a significance of 4.5sigma. In a subsequent fit to the region with mK+K- > 1.1 GeV/c2, we find ACP = -0.054 +/- 0.102 +/- 0.060 and betaeff = 0.436 +/- 0.087+0.055-0.031 rad, excluding the possibility that betaeff = 0 at 5.1sigma. We use the data with mK+K - < 1.1 GeV/c2 to extract CP asymmetries separately for B 0 decays to &phis;(1020)K0 and f0(980)K0, finding beta eff,&phis;=0.11 +/- 0.14 +/- 0.06 and beff,f0 =0.14 +/- 0.15 +/- 0.05. |