Muon pair production in the process e+e- → e+e- μ+μ- is studied using the data taken at LEP1 (√s ≃ mz) with the DELPHI detector during the years 1992-1995. The corresponding integrated luminosity is 138.5 pb-1. The QED predictions have been tested over the whole Q2 range accessible at LEP1 (from several GeV2/c4 to several hundred GeV2/c4) by comparing experimental distributions with distributions resulting from Monte Carlo simulations using various generators. Selected events are used to extract the leptonic photon structure function Fγ 2. Azimuthal correlations are used to obtain information on additional structure functions, Fγ A and Fγ B, which originate from interference terms of the scattering amplitudes. The measured ratios Fγ A/Fγ 2 and FγB/Fγ 2 are significantly different from zero and consistent with QED predictions.