Abstract: --------- This thesis presents a measurement of the time-dependent asymmetry in the rate of $\overline{B}{^0_d}$ versus $B^0_d$ decays to $J/\psi K^0_S$. In the context of the Standard Model this is interpreted as a measurement of the $CP$ violation parameter $\sin(2\beta)$. A total of $198\pm 17$ $B^0_d/\overline{B}{^0_d}$ decays were observed in $p\bar{p}$ collisions at $\sqrt{s} = 1.8$ TeV by the CDF detector at the Fermilab Tevatron. The initial $B$ flavor (whether $\BZ$ or $\BZB$) is determined by a same-side flavor tagging technique. The analysis results in $\sin(2\beta) = 1.8\pm 1.1\,{\rm (stat.)}\pm 0.3\,{\rm (syst.)}$. This analysis demonstrates the feasibility of studying $CP$ violation in the $\BZ$--$\BZB$ system at a hadron collider. By applying the methods used in this analysis, future, higher-statistics experiments should be able to tightly constrain the parameters of the Standard Model. Portions of this analysis have been submitted for Publication. The article ``{Measurement of the $B^0_d$-$\overline{B}{^0_d}$ flavor oscillation frequency and study of same side flavor tagging of $B$ mesons in $p\bar p$ collisions}'' has been submitted to {\em Phys. Rev. D}; the preprint for this article is {\bf FERMILAB-Pub-98/188-E}. The article ``{Measurement of the $CP$-Violation Parameter $\sin(2\beta)$ in $B^0_d/\overline{B}{^0_d} \rightarrow J/\psi K^0_S$ Decays}'' has been submitted to {\em Phys. Rev. Lett.}; the preprint for this article is {\bf FERMILAB-Pub-98/189-E}. Posted to /cdf/pub/thesis/cdf4767_Measurement_sin2beta.ps http://www-cdf.fnal.gov/thesis/cdf4767_Measurement_sin2beta.ps Posted by kkelley@cdfsga