n the Standard Model of fundamental particles, the existence of a doublet of boson fields is postulated in order for particle masses to be generated through spontaneous symmetry breaking. The Higgs boson (H°) is the remnant of this doublet after spontaneous symmetry breaking has occurred. A search for the Higgs boson has been performed with data from electron- positron collisions collected by the OPAL detector at LEP. The search was made for signals of the type e+ + e- → (e+e- or μ+μ-)+0, known as the leptonic channel; and vv + H0 known as the neutrino channel. This thesis reports on the results obtained, and describes the leptonic channel analyses in detail. The analyzed data was taken at the centre-of-mass energies between 88 and 95 GeV in the years 1990-1993 and represented a luminosity of 78pb-1. When combined with previous OPAL results, the present study excludes the existence of a Standard Model Higgs boson with mass below 56.9 GeV at 95% confidence level. The results of this study were published in Physics Letters B in March 1994.