The top quark is the heaviest elementary particle. Its mass is one of the fundamental parameters of the standard model of particle physics, and an important input to precision electroweak tests. This thesis describes three measurements of the top-quark mass in the dilepton decay channel. The dilepton events have two neutrinos in the final state; neutrinos are weakly interacting particles that cannot be detected with a multipurpose experiment. Therefore, the signal of dilepton events consists of a large amount of missing energy and momentum carried off by the neutrinos. The top-quark mass is reconstructed for each event by assuming an additional constraint from a top mass independent distribution. Template distributions are constructed from simulated samples of signal and background events, and parametrized to form continuous probability density functions. The final top-quark mass is derived using a likelihood fit to compare the reconstructed top mass distribution from data to the parametrized templates. One of the analyses uses a novel technique to add top mass information from the observed number of events by including a cross-section-constraint in the likelihood function. All measurements use data samples collected by the CDF II detector.
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