The QED structure of the photon The structure of both quasi-real and highly virtual photons is investigated using the reaction e+e- --> e+e- mu+mu-, proceeding via the exchange of two photons. The results are based on the complete OPAL dataset taken at e+e- centre-of-mass energies close to the mass of the Z boson. The QED structure function and the differential cross-section for quasi-real photons are obtained as functions of the fractional momentum x from the muon momentum which is carried by the struck muon in the quasi-real photon for values of Q^2 ranging from 1.5 to 400 GeV^2. The differential cross-section for highly virtual photons is measured for 1.5 < Q^2 < 30 GeV^2 and 1.5 < P^2 < 20 GeV^2, where Q^2 and P^2 are the negative values of the four-momentum squared of the two photons such that Q^2 > P^2. Based on azimuthal correlations the QED structure functions for quasi-real photons are determined for an average Q^2 of 5.4 GeV^2. Parallel session : 2 Plenary session :12