The purpose of high energy physics is to improve our knowledge about the fundamental structure of matter, in particular about particles that constitute the world. One of these is the top quark, that was discovered in 1995 by the CFD and D0 collaborations at the Tevatron protons-antiprotons collider. One of the primary aim of the Tevatron has been then the fine study of the top quark propertiers, in particular the top-antitop production cross section. SDifferent analysis have been performed in the leptons, dileptons, and all-hadronic channels to determine accurately the values of these parmatersn and thus to test the validity of the Standard Model.The main goal of this thesis is to verify one of the theoretical predictions of the Standard Model of particle physics, the top-antitop production cross section, at the Tevatron collider. The channel studied is constituted by one muon, one tau lepton, their associated neutrinos, and two b-jets (one coming from the quark, the other one coming from a b anti-quark). The reconstruction and identification of jets, of muons, of taus (in particular with the use of a taus neural network), and the b-tagging of jets, represent the fundamental elements of this study. Endly, a good agreement between data and Monte Carlo simulation is obtained at the final stage of analysis. Moreover, the final measurement and the theoretical prediction at the NLL+NLO perturbations level are found to be compatible.
