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Di-jet producion is studied in collisions of quasi-real photons at e+e-centre- of-mass energies sqrt(s)ee from 189 to 209 GeV at LEP. The data werecollected with the OPAL detector. Jets are reconstructed using an inclusive k_tclustering algorithm for all cross-section measurements presented. A cone jetalgorithm is used in addition to study the different structure of the jetsresulting from either of the algorithms. The inclusive di-jet cross-section ismeasured as a function of the mean transverse energy Etm(jet) of the twoleading jets, and as a functiuon of the estimated fraction of the photonmomentum carried by the parton entering the hard sub-process, xg, for differentregions of Etm (jet). Angular distribution in di-jet events are measured andused to demonstrate the dominance of quark and gluon initiated processes indifferent regions of phase space. Furthermore the inclusive di-jetcross-section as a function of |eta(jet)| and |delta eta (jet)| is presentedwhere eta(jet) is the jet pseudo-rapidity. Different regions of the xg+ -xg--space are explored to study and control the influence of an underlying event.The results are compared to next-to-leading order perturbative QCD calculationsand to the predictions of the leading order Monte Carlo generator PYTHIA.Comment: 45 pages, 16 figure

Di-jet production in photon-photon collisionsat $\sqrt{s_{\protect\bf\mathrm{ee}}}$ from 189 to 209 GeV