Energy levels, radiative rates, collision strengths, and effective collision strengths for all transitions up to and including the n=5 levels of Al XIII have been computed in the jj coupling scheme including relativistic effects. All partial waves with angular momentum J<=60 have been included, and resonances have been resolved in a fine energy grid in the threshold region. Collision strengths are tabulated at energies above thresholds in the range 170.0<=E<=300.0Ryd, and results for effective collision strengths, obtained after integrating the collision strengths over a Maxwellian distribution of electron velocities, are tabulated over a wide temperature range of 4.4<=logT_e_<=6.8K. The importance of including relativistic effects in a calculation is disc ussed in comparison with the earlier available non-relativistic results.