This thesis presents results of an analysis of muon pair production by two-photon interactions, through the study of the reaction ee-->eeuu. The analysis was performed using data from the PLUTO detector situated in the e+e- storage-ring accelerator, PETRA. A total of 681 events were selected where at least one of the scattered beam electrons was detected. The data correspond to a total integrated luminosity of ~35 pb-1 for a beam energy of 17.5 GeV. The main objective of the analysis was to test the 4 validity of a higher order (O(alpha4) calculation in quantum electrodynamics (QED), over a large kinematic range. The scattered electron was detected over a wide angular acceptance, resulting in a range of virtual photon mass squared, -Q2, from 0.1 to 100 GeV2. A detailed comparison was made between distributions of variables obtained from the data and the theoretical calculations. Corrections due to background contamination and radiative effects were also considered. Measurements were also made, concerning the sub-process by extracting the leptonic photon structure function and the total ross-section in the case where a virtual and quasi-real photon collide. The QED calculation for di-muon production by two- photon interactions is seen to describe the data well for di-muon invariant masses greater than 1.2 GeV. For lower values of invariant mass, a further contribution from di-muon production by virtual bremsstrahlung seems evident in the high data between 20 to 100 GeV2. In conclusion then, there are no unexpected deviations from the higher order QED calculations relevant to this analysis.