Abstract
Results on B physics and heavy quarkonia production based on data collected during the Tevatron run Ia and Ib are presented. For B physics, results on B meson man measurement, B meson lifetimes, rare decay searches, B{sup o} {bar B} {sup o} mixing and B meson polarization are discussed. Accuracies comparable to those of leading e{sup +} e{sup {minus}} experiments are attained or expected to be attained by the end of Tevatron Run I in almost all these fields. features of J/{psi}, {psi}((2S), {chi}c, and {Upsilon} bound state production are also discussed.
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