The work in this thesis is focused on molecules that are able to self-assemble on different surfaces by forming two-dimensional templates stabilised via double or triple hydrogen bonding. In particular, assemblies of molecules such as melamine, perylene tetra-carboxylic di-imide (PTCDI), perylene tetra-carboxylic di-anhydride (PTCDA), naphthalene tetracarboxylic-dianhydride (NTCDA) and naphthalene tetracarboxylic diimide (NTCDI) are studied in detail. The aim is to give a complete characterisation of the supramolecular networks, taking into account the balance between the molecule-molecule and molecule-substrate interactions. All our assembly calculations are done within the gas phase approximation, i.e. without taking into account the surface, which is a good approximation assuming that the molecules are quite mobile on the surface. Using a systematic method based on considering all possible hydrogen bond connections between the molecules we investigate planar superstructures that organic molecules can form in one and two dimensions. The structures studied are based on two or more molecules per unit cell and all structures considered, assemble in flat periodic patterns. Most of the calculations are performed using the density functional theory method. We show that the calculated lattice parameters of the structures considered compare well with those measured experimentally. To specifically check the applicability of the gas-phase approximation, we systematically investigated the adsorption of the molecules on the Au(111) metal surface with the particular attention being paid to the characterisation of the potential energy surface of our molecules on this surface. We performed these calculations using both a conventional functional (PBE) which does not include the dispersion interaction, and the newly developed vdW-DF method which does. We find that the adsorption energies of these flat molecules on the metal surface calculated with the vdW-DF method are effected significantly by the dispersion interaction and depend linearly on the size of the molecules. While the PBE method predicts very weak adsorption energies which do not depend on the sizes of the molecules, the vdW-DF method gives strong binding entirely due to the dispersion interaction. We found that both PBE and vdW-DF methods predict a very small corrugation of the total energy of the molecules on gold. These results support our main assumption of the molecule-surface interaction changing little laterally and resulting in a mobility of the molecules at room temperature on the surface, i.e. the gas-phase modelling is a good approximation for the Au(111) surface.