At the Tevatron Collider at Fermilab, a large number of top quarks have been produced in the ongoing run. The CDF and DZero collaborations have made first measurements of the ttbar cross section in several decay channels, and have measured the top quark mass. In addition, they have set new limits on the cross sections for single top quark production, and have started to measure some of the properties of the top quark via studies of its decays. This paper summarizes the status of these measurements and discusses where they are heading in the next few years. The paper is based on a talk I gave at the Rencontres du Vietnam in Hanoi, August 2004; the results have been updated to show the latest values and new measurements.
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