We present a measurement of the top quark mass using $t\bar{t}$ pair creation events decaying into the lepton + jets channel in $p\bar{p}$ collisions at $\sqrt{s}=1.96 ~ {\rm TeV}$. The data sample used in this analysis was collected with the Collider Detector at Fermilab (CDF) in Tevatron Run II during the period from March 2002 through August 2003. Tagging the jets originating from $b$ quarks not only helps reduce the background events but also plays an important role in the correct reconstruction of the $t\bar{t}$ event. Our analysis subdivides the candidate events into three categories - 0, 1 and 2 tag channels - by the numbers of $b$-tagged jets in the events. The categorization of the events has been optimized for the best sensitivity for the top quark mass. The accumulated integrated luminosities for each channel were : $193 ~ {\rm pb^{-1}}$ for 0 tag, and $162 ~ {\rm pb^{-1}}$ for 1 and 2 tag channels. We found eleven $t\bar{t}$ candidate events in 2 tag, seventeen in 1 tag and forty events in 0 tag channel. We extracted a top mass of $180.9~^{+6.4}_{-6.0}~({\rm stat})~ \pm 5.8~ ({\rm syst}) ~ {\rm GeV/}c^2$ using 2 tag candidate events, and a combined top mass of $177.2~^{+4.9}_{-4.7}~({\rm stat})~ \pm 6.6~ ({\rm syst}) ~ {\rm GeV/}c^2$ using the total sixty-eight candidate events in the three channels. Posted to /cdf/pub/thesis/cdf7625_cdf7625.ps http://www-cdf.fnal.gov/thesis/cdf7625_cdf7625.ps Posted by doraemon