This dissertation describes the measurement of the average B hadron lifetime using a high statistics sample of B--> J/psi X decays produced in proton antiproton collisions at a center of mass energy of 1.8 TeV at the Fermilab Tevatron. The integrated luminosity of the sample is 10.1 pb-1 recorded with the Collider Detector at Fermilab (CDF). In this analysis the decay vertex of the decay J/psi -->mu^+ mu^-$ as reconstructed by a silicon vertex detector is used to extract the lifetime from the data. We find the following value for the average b hadron lifetime: [ tau_{B} = 1.46 pm 0.06; (stat.); pm 0.06; (syst.); ps] This is the first measurement of the b-hadron lifetime at a hadron collider. It demonstrates that it is possible to access the large b-quark production cross section in $poverline{p}$ collisions and to achieve high statistics even in modes which have small product branching ratios as in this case: $BR(Brightarrow J/psi X) cdot BR(J/psi rightarrow mu^+ mu^-) = 7.7 times 10^{-4}$.

Measurements of the average b-hadron lifetime using inclusive B [yields] J/[psi]X events, the individual B[sub u] and B[sub d] lifetimes and their ratio using exclusive B [yields] [psi]K events, and the B[sub s] lifetime using semileptonic B[sub s] lifetime using semileptonic B[sub s] [yields] l[nu]D[sub 3]X events are presented. The results were obtained from a 21.3 pb[sup [minus]1] sample of [radical]s = 1.8 TeV [bar p]p collisions collected in 1992--93 at the Fermilab Tevatron collider and required the precise position measurements of the recently installed CDF silicon vertex detector.

Two measurements of the lifetime of neutral and charged B mesons in p[bar p] collisions at[radical]s= 1.8 TeV by the CDF experiment are presented. The first relies on the study of exclusive decays of the type B[yields][psi] K, the second on semileptonic decays of a B meson into a D[degrees] or a D. The combined results are[tau](B[sup+])= 1.62[+-] 0.09 ps, [tau](B[sub 0])= 1.60[+-] 0.09 ps and[tau](B[sup+])/[tau](B[sup 0])= 1.00[+-] 0.07.

The two collider experiments at the Tevatron, CDF and D0, have made a lot of progress in B{sub s} lifetime difference measurements. Here, they have included 3 different channels of measurements, namely, B{sub s} {yields} J/{psi} + {phi}, B{sub s} {yields} K{sup +}K{sup -} and B{sub s} {yields} D{sub s}{sup (*)+}D{sub s}{sup (*)-}. Combining all the available measurements, they have obtained {Delta}{Lambda}{sub s} = 0.097{sub -0.042}{sup +0.041} ps{sup -1} and {bar {tau}} = 1/{Lambda}{sub s} = 1.461 {+-} 0.030 ps. {Delta}{Lambda}{sub s} is now 2.3 {sigma} away from zero.