In this thesis a direct search for the Standard Model Higgs boson production in association with a W boson at the CDF detector in the Tevatron is presented. This search contributes predominantly in the region of low mass Higgs region, when the mass of Higgs boson is less than about 135 GeV. The search is performed in a final state where the Higgs boson decays into two b quarks, and the W boson decays leptonically, to a charged lepton (it can be an electron or a muon) and a neutrino. This work is organized as follows. Chapter 2 gives an overview of the Standard Model theory of particle physics and presents the SM Higgs boson search results at LEP, and the Tevatron colliders, as well as the prospects for the SM Higgs boson searches at the LHC. The dataset used in this analysis corresponds to 4.8 fb−1 of integrated luminosity of p{bar p} collisions at a center of mass energy of 1.96 TeV. That is the luminosity acquired between the beginning of the CDF Run II experiment, February 2002, and May 2009. The relevant aspects, for this analysis, of the Tevatron accelerator and the CDF detector are shown in Chapter 3. In Chapter 4 the particles and observables that make up the WH final state, electrons, muons, E{sub T}, and jets are presented. The CDF standard b-tagging algorithms to identify b jets, and the neural network flavor separator to distinguish them from other flavor jets are also described in Chapter 4. The main background contributions are those coming from heavy flavor production processes, such as those coming from Wbb, Wcc or Wc and tt. The signal and background signatures are discussed in Chapter 5 together with the Monte CArlo generators that have been used to simulate almost all the events used in this thesis. WH candidate events have a high-p{sub T} lepton (electron or muon), high missing transverse energy, and two or more than two jets in the final state. Chapter 6 describes the event selection applied in this analysis and the method used to estimate the background contribution. The Matrix Element method, that was successfully used in the single t0p discovery analysis and many other analyses within the CDF collaboration, is the multivariate technique used in this thesis to discriminate signal from background events. With this technique is possible to calculate a probability for an event to be classified as signal or background. These probabilities are then combined into a discriminant function called the Event Probability Discriminant, EPD, which increases the sensitivity of the WH process. This method is described in detail in Chapter 7. As no evidence for the signal has been found, the results obtained with this work are presented in Chapter 8 in terms of exclusion regions as a function of the mass of the Higgs boso, taking into account the full systematics. The conclusions of this work to obtain the PhD are presnted in Chapter 9.