We have studied the First stages leading to the formation of self-assembled monolayers of S-cysteine molecules adsorbed on a Au(111) surface. Density functional theory (DFT) calculations for the adsorption of individual cysteine molecules on Au(111)at room temperature show low-energy barriers all over the 2D Au(111) unit cell. As a consequence, cysteine molecules diffuse freely oil the Au(111) Surface and they can be regarded as a 2D molecular gas. The balance between molecule-molecule and molecule-substrate interactions induces molecular condensation and evaporation from the morphological surface structures (steps, reconstruction edges, etc.) as revealed by scanning tunnelling microscopy (STM) images. These processes lead progressively to the formation of a number of stable arrangements, not previously reported, such as single-molecular rows, trimers, and 2D islands. The condensation of these structures is driven by the aggregation of new molecules, stabilized by the formation of electrostatic interactions between adjacent NH3+ and COO- groups, together with adsorption at a slightly more favorable quasi-top site of the herringbone Au reconstruction.