We discuss the measurement of the cross section for t{bar t} production in p{bar p} collisions at {radical}s = 1.96 TeV in e+jets final states observed at the D0 experiment at the Fermilab Tevatron. Our result is based on data collected from the June 2002 to September 2003 period of Run II of the p{bar p} Collider. In the Standard Model, the top quark is expected to decay mainly into a W boson and a b quark. The W boson can decay subsequently into a lepton and its neutrino or a q{bar q} quark-antiquark pair. In this thesis, we focus on the e{sup +} {nu}{sub e} or e{sup -} {bar {nu}}{sub e} decays of one of the W bosons and the q{bar q} decays of the other W boson in t{bar t} final states. The b, q and q' quarks appear as jets of particles in the detector, thereby defining the e+jets final state. We present two methods used for performing this measurement. The first method is based on a Random Grid Search (RGS) that minimizes the uncertainty on the extracted cross section. The variables used in the search take advantage of differences between expected background and signal processes to obtain the yield of t{bar t} events. The second method uses a Neural Network (NN) procedure that discriminates signal from background through the application of a NN trained on simulated t{bar t} signal and W+jets background events. The preliminary results presented in this thesis for inclusive t{bar t} production are {sigma}{sub p{bar p} {yields} t{bar t} + x} of 7.9{sub -2.4}{sup +2.6}(stat) {sub -2.3}{sup +2.2}(syst) {+-} 0.5 (L) pb for the NN analysis, where the uncertainties correspond to contributions from statistical and systematic sources and from the uncertainty on luminosity. Our measurements are consistent with each other, and are within error of the value of 6.77 {+-} 0.42 pb expected in the Standard Model.