Di-jet production is studied in collisions of quasi-real photons at e + e- centre-of-mass energies s\protectee−−−−−−−√ from 189 to 209 GeV at LEP. The data were collected with the OPAL detector. Jets are reconstructed using an inclusive k⊥ -clustering algorithm for all cross-section measurements presented. A cone jet algorithm is used in addition to study the different structure of the jets resulting from either of the algorithms. The inclusive di-jet cross-section is measured as a function of the mean transverse energy E¯jetT of the two leading jets, and as a function of the estimated fraction of the photon momentum carried by the parton entering the hard sub-process, xγ , for different regions of E¯jetT . Angular distributions in di-jet events are measured and used to demonstrate the dominance of quark and gluon initiated processes in different regions of phase space. Furthermore the inclusive di-jet cross-section as a function of ηjet and Δηjet is presented, where ηjetcntr is the jet pseudo-rapidity. Different regions of the x+γ - x−γ -space are explored to study and control the influence of an underlying event. The results are compared to next-to-leading order perturbative QCD calculations and to the predictions of the leading order Monte Carlo generator PYTHIA.