NGC 6537 is an unusually high excitation point symmetric planetary nebula with a rich spectrum. Its kinematical structures are of special interest. We are here primarily concerned with the high resolution spectrum as revealed by the Hamilton echelle Spectrograph at Lick Observatory (resolution ≈ 0.2 Å) and supplemented by UV and near-UV data. These extensive data permit a determination of interstellar extinction, plasma diagnostics, and ionic concentrations. The photoionization models that have been used successfully for many planetary nebulae are not entirely satisfactory here. The plasma electron temperature of a photoionization model cannot much exceed 20,000 K, but plasma diagnostics show that regions emitting radiation of highly ionized atoms such as [Neiv] and [Nev] are much hotter, showing that shock excitation must be important, as suggested by the remarkable kinematics of this object. Hence, instead of employing a strict photoionization model, we are guided by the nebular diagnostics, which reveal how electron temperature varies with ionization potential and accommodates density effects. The predictions of the photoionization model may be useful in estimating ionization correction factor. In effect, we have estimated the chemical composition by using both photoionization and shock considerations.