In this thesis, we rst study the lagrangian formulation of gauge theories, QED, Yang-rnMills theory and the Glashow-Weinberg-Salam model for Electroweak interaction. Wernthen, we use the framework of Bethe-Salpeter equation (BSE) under Covariant Instan-rntaneous Ansatz (CIA) to calculate the leptonic decays of B-meson. The structure ofrnhadron-quark vertex function À€€(^q) is obtained from BSE under CIA, while the structurernof q qWð€€€ vertex is obtained from GWS model for Electroweak interactions. We derive for-rnmulas for the decay constant fB of B-meson. We obtain the numerical values of the decayrnconstant, fB of the B-meson as well as its decay width. Then the results are comparedrnwith existing experimental results