The first question to settle is what the classical theory will be. As most of the work that has been done has been limited to the plane, this presentation will also be restricted to that particular case (in most proposals the extension to higher dimensional geometries is considered to be completely straightforward). But that is not sufficient, for there are different routes to follow as to the presentation of plane geometry. One possibility is to take any axiomatisation of the (Euclidean) plane—say, Hilbert’s formulation of 1899 in his Grundlagen der Geometrie—and show what changes are required to have (a) finite models of the axiomatic theory, and (b) finite models that approximate the classical (infinite, Euclidean) models as closely as possible. One of the very first attempts dates back to the late 40s, early 50s and will therefore be presented here as an exemplar (in the sense that it has both all the positive qualities required as well as the oddities that seem to go together with such attempts). More specifically, it concerns the work of Paul Kustaanheimo in partial collaboration with G. Järnefelt in the period between 1949 and 1957. Next a recent proposal will be discussed, along totally different lines, of Patrick Suppes and a somewhat older proposal of Ludwik Silberstein, where the geometry is directly imbedded in a physical theory, special relativity theory to be precise. The concluding section of this part deals with some specific problems and tentative solutions.