Considerable progress has been made recently in the study of the adsorption of gaseous molecules in a monolayer on a solid surface, when the molecules are attached to fixed locations on that surface and allowance is made for interaction between the adsorbed molecules. It has been shown in particular that, if there is an attractive field between two adsorbed molecules so that two adsorbed molecules in neighbouring locations are more tightly bound than when they are adsorbed separately at a distance, the adsorption isotherm shows critical phenomena. This feature of the isotherm may be used to give a generally successful interpretation of the well-known critical condensation phenomena discussed first in this manner by Langmuir and Frenkel. A recent example of experiments on this phenomenon is to be found in the work of Cockcroft on the deposition of cadmium on copper. The work of Peierls, who uses Bethe's method for approximating to the partition function for the adsorbed layer, shows in the most convincing way how interactions between neighbours in the single layer lead to critical phenomena for the degree of completion of the layer.