Molecular dynamics simulations were used to investigate aggregation of surfactants at the solid liquid interface at different surfactant concentrations. For these studies simulations of the sodium dodecyl sulfate (SDS) surfactant with a graphite surface were carried out. At low concentrations the SDS molecules aggregated in slices of cylinders attached to the solid surface, whereas at slightly higher concentrations the structures showed irregular shapes. When the concentration was again increased to a higher value, the molecules aggregated in a more complex structure, an irregular aggregate on the top of a semicylinder adsorbed on the graphite surface. From the present results more insights about the internal structure of the aggregates were observed than in actual experiments, e.g., it was found that the SDS tails arrayed in well-defined layers close to the graphite surface. More over, from the internal structure it was possible to show a structural transition driven by an increment in the surfactant concentration which, to the best of our knowledge, has not been studied from a molecular point of view. Therefore the transition was studied in terms of the height of the structures. Along with these studies adsorption of the aggregates, by calculating contact angles, and adsorption isotherms were also analyzed. Finally, investigations of the surface coverage with the concentration showed that this quantity did not change considerably with the concentration.