In this thesis we rst give a Lagrangian formulation of the gauge theories QEDrnand QCD. We derive the Feynman rules for QCD . AS an application of the rule, wern rst present the calculation of cross section for the process q+ q ! g+g as a mathematicalrnpreliminary. We then derive the 2-particle Bethe-Salpeter equation. Then we evaluate therncross section for the production of double heavy quarkonium production in high energyrnelectron-positron collisions at the center of mass energyrnprns 10.6 GeV. The cross sectionrnfor the process of e+eÀ€€ ! J= + c at the stated energy has been calculated by applyingrnthe two-particle Bethe-Salpeter wave equation. We have used the heavy quark limitrnand calculated the cross section for the lowest order diagram. The results are in broadrnagreement with the Belle's data available recently