The question of the nature and principles of the universe and our place in it is the driving force of science since Mesopotamian astronomers glanced for the first time at the starry sky and Greek atomism has been formulated. During the last hundred years modern science was able to extend its knowledge tremendously, answering many questions, opening entirely new fields but as well raising many new questions. Particularly Astronomy, Astroparticle Physics and Particle Physics lead the race to answer these fundamental and ancient questions experimentally. Today it is known that matter consists of fermions, the quarks and leptons. Four fundamental forces are acting between these particles, the electromagnetic, the strong, the weak and the gravitational force. These forces are mediated by particles called bosons. Our confirmed knowledge of particle physics is based on these particles and the theory describing their dynamics, the Standard Model of Particles. Many experimental measurements show an excellent agreement between observation and theory but the origin of the particle masses and therefore the electroweak symmetry breaking remains unexplained. The mechanism proposed to solve this issue involves the introduction of a complex doublet of scalar fields which generates the masses of elementary particles via their mutual interactions. This Higgs mechanism also gives rise to a single neutral scalar boson with an unpredicted mass, the Higgs boson. During the last twenty years several experiments have searched for the Higgs boson but so far it escaped direct observation. Nevertheless these studies allow to further constrain its mass range. The last experimental limits on the Higgs mass have been set in 2001 at the LEP collider, an electron positron machine close to Geneva, Switzerland. The lower limit set on the Higgs boson mass is m{sub H}> 114.4 GeV/c2 and remained for many years the last experimental constraint on the Standard Model Higgs Boson due to the shutdown of the LEP collider and the experimental challenges at hadron machines as the Tevatron. This thesis was performed using data from the D0 detector located at the Fermi National Accelerator Laboratory in Batavia, IL. Final states containing two electrons or a muon and a tau in combination with missing transverse energy were studied to search for the Standard Model Higgs boson, utilizing up to 4.2 fb−1 of integrated luminosity. In 2008 the CDF and D0 experiments in a combined effort were able to reach for the first time at a hadron collider the sensitivity to further constrain the possible Standard Model Higgs boson mass range. The research conducted for this thesis played a pivotal role in this effort. Improved methods for lepton identification, background separation, assessment of systematic uncertainties and new decay channels have been studied, developed and utilized. Along with similar efforts at the CDF experiment these improvements led finally the important result of excluding the presence of a Standard Model Higgs boson in a mass range of m{sub H} = 160-170 GeV/c2 at 95% Confidence Level. Many of the challenges and methods found in the present analysis will probably in a similar way be ingredients of a Higgs boson evidence or discovery in the near future, either at the Tevatron or more likely at the soon starting Large Hadron Collider (LHC). Continuing to pursue the Higgs boson we are looking forward to many exciting results at the Tevatron and soon at the LHC. In Chapter 2 an introduction to the Standard Model of particle physics and the Higgs mechanism is given, followed by a brief outline of existing theoretical and experimental constraints on the Higgs boson mass before summarizing the Higgs boson production modes. Chapter 3 gives an overview of the experimental setup. This is followed by a description of the reconstruction of the objects produced in proton-antiproton collisions in Chapter 4 and the necessary calorimeter calibrations in Chapter 5. Chapter 6 follows with an explanation of the phenomenology of the proton-antiproton collisions and the data samples used. In Chapter 7 the search for the Standard Model Higgs boson using a di-electron final state is discussed, followed by the analysis of the final states using muons and hadronic decaying taus in Chapter 8. Finally a short outlook for the prospects of Higgs boson searches is given in Chapter 9.