Low energy electron diffraction analyses of materials physisorbed on a graphite single crystal reveal that ordered structures are common in the monolayer range under the accessible p, T conditions. Data are presented for the lattice gas and 2D liquid as well as the 2D crystal phases. A characteristic density distribution due to ion repulsion appears to have been observed with Br 2 and Cs in the lattice gas phase. Where lateral interactions are weak (Xe, Br 2, Cs, C 6H 3Br 3, GeI 4) the 2D crystal phase or phases exist in a limited high coverage range. Transitions occur that are probably due to change in vibrational mode (Br 2). Where lateral forces are stronger (As 2O 3, FeCl 3, ZnI 2, and GeI 2 with ionic bonding in the layer) clustering to form 2D crystallites occurs at low or intermediate coverage. Structure determination often does not depend on detailed diffraction analysis. In some cases transitions from gas to liquid or liquid to solid did not occur abruptly, that is, they appeared to be 2nd order. Ordered monolayer structures were not obtained from several other materials tested. Recrystallization phenomena appeared frequently. The transition to multilayers usually produced patterns characterized by extensive disorder, partly because the 2D phase is often not simply related to the bulk structure. Desorption by the electron beam was observed but was not a serious factor. Such results have direct application to catalysis, physisorption displacement reaction, isotherm analysis, surface area determination, etc.