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In 1995 the last missing member of the known families of quarks, the top quark, was discovered by the CDF and D0 experiments at the Tevatron, a proton-antiproton collider at Fermilab near Chicago. Until today, the Tevatron is the only place where top quarks can be produced. The determination of top quark production and properties is crucial to understand the Standard Model of particle physics and beyond. The most striking property of the top quark is its mass--of the order of the mass of a gold atom and close to the electroweak scale--making the top quark not only interesting in itself but also as a window to new physics. Due to the high mass, much higher than of any other known fermion, it is expected that the top quark plays an important role in electroweak symmetry breaking, which is the most prominent candidate to explain the mass of particles. In the Standard Model, electroweak symmetry breaking is induced by one Higgs field, producing one additional physical particle, the Higgs boson. Although various searches have been performed, for example at the Large Electron Positron Collider (LEP), no evidence for the Higgs boson could yet be found in any experiment. At the Tevatron, multiple searches for the last missing particle of the Standard Model are ongoing with ever higher statistics and improved analysis techniques. The exclusion or verification of the Higgs boson can only be achieved by combining many techniques and many final states and production mechanisms. As part of this thesis, the search for Higgs bosons produced in association with a top quark pair (t{bar t}H) has been performed. This channel is especially interesting for the understanding of the coupling between Higgs and the top quark. Even though the Standard Model Higgs boson is an attractive candidate, there is no reason to believe that the electroweak symmetry breaking is induced by only one Higgs field. In many models more than one Higgs boson are expected to exist, opening even more channels to search for charged or neutral Higgs bosons. Depending on its mass, the charged Higgs boson is expected to decay either into top quarks or be the decay product of a top quark. For masses below the top quark mass, the top decay into a charged Higgs boson and a b quark can occur at a certain rate, additionally to the decays into W bosons and a b quark. The different decays of W and charged Higgs bosons can lead to deviations of the observed final number of events in certain final states with respect to the Standard Model expectation. A global search for charged Higgs bosons in top quark pair events is presented in this thesis, resulting in the most stringent limits to-date. Besides the decay of top quarks into charged Higgs or W bosons, new physics can also show up in the quark part of the decay. While in the Standard Model the top quark decays with a rate of about 100% into a W boson and a b quark, there are models where the top quark can decay into a W boson and a non-b quark. The ratio of branching fractions in which the top quark decays into a b quark over the branching fractions in which the top quark decays into all quarks is measured as part of this thesis, yielding the most precise measurement today. Furthermore, the Standard Model top quark pair production cross section is essential to be known precisely since the top quark pair production is the main background for t{bar t}H production and many other Higgs and beyond the Standard Model searches. However, not only the search or the test of the Standard Model itself make the precise measurement of the top quark pair production cross section interesting. As the cross section is calculated with high accuracy in perturbative QCD, a comparison of the measurement to the theory expectation yields the possibility to extract the top quark mass from the cross section measurement. Although many dedicated techniques exist to measure the top quark mass, the extraction from the cross section represents an important complementary measurement. The latter is briefly discussed in this thesis and compared to direct top mass measurements. The goal of this thesis is the improved understanding of the top quark sector and its use as a window to new physics. Techniques are extended and developed to measure the top quark pair production cross section simultaneously with the ratio of branching fractions, the t{bar t}H cross section or the rate with which top quarks decay into charged Higgs bosons. Some of the results are then taken to extract more information. The cross section measurement is used to extract the top quark mass, and the ratio of the top quark pair production cross sections in different final states, yielding a limit on non-Standard Model top quark decays.
