Di-jet production is studied in collisions of quasi-real photons at e(+)e(-) centre-of-mass energies roots(ee) from 189 to 209 GeV at LEP. The data were collected with the OPAL detector. Jets are reconstructed using an inclusive k(perpendicular to)-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) over bar (jet)(T) 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, x(gamma), for different regions of (E) over bar (jet)(T). 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 \eta(jet)\ and \Deltaeta(jet)\ I is presented, where eta(jet) is the jet pseudo-rapidity. Different regions of the x(gamma)(+)-x(gamma)(-)-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.