The monolayer formed at an air/water interface by the synthetic non-ionic surfactant, 1,2-di-O-octadecyl-rac-glyceryl-3-(omega-methoxydodecakis (ethylene glycol)) (2C18E12) has been characterized using Langmuir trough measurements, Brewster angle microscopy (BAM), and neutron reflectometry. The BAM and reflectometry studies were performed at four different surface pressures (pi) in the range 15-40 mN/m. The BAM studies (which give information on the in-plane organisation of the surfactant layer) demonstrate that the 2C18E12 molecules are arranged on the water surface to form distinct, approximately circular, 5 microm diameter domains. As the surface pressure is increased these domains retain their size and shape but are made progressively more close-packed, such that the monolayer is made more or less complete at pi=40 mN/m. The neutron reflectometry measurements were made to determine the structure of the interfacial surfactant layer at pi=15, 28, 34 and 40 mN/m, providing information on the thickness of the 2C18E12 alkyl chains', head groups' and associated solvent distributions (measured along the surface normal), along with the separations between these distributions, and the effective interfacial area per molecule. Partial structure factor analyses of the reflectivity data show that the effective interfacial area occupied decreases from 217 A2 per 2C18E12 molecule at pi=15 mN/m down to 102 A2 at pi=40 mN/m. There are concomitant increases in the widths of the surfactant's alkyl chains' and head groups' distributions (modelled as Gaussians), with the former rising from 12 A (at pi=15 mN/m) up to 19 A (at pi=40 mN/m) and the latter rising from 13 A (at pi=15 mN/m) up to 24 A (at pi=40 mN/m). The compression of the monolayer is also shown to give rise to an increased surface roughness, some of which is due to the thermal roughness caused by capillary waves, but with a significant contribution also coming from the intrinsic/structural disorder in the monolayer. At all surface pressures studied, the alkyl chains and head groups of the 2C18E12 are found to exhibit a significant overlap, and this increases with increasing pi. Given the various trends noted on how the structure of the 2C18E12 monolayer changes as a function of pi, we extrapolate to consider the structure of the monolayer at pi>40 mN/m (making comparison with its single chain (CnEm) counterparts) and then relate these findings to the observations recorded on the structure and solute entrapment efficiency of 2C18E12 vesicles.