Self-assembly/self-aggregation of surfactant molecules in bulk and the vicinity of a surface has been a topic of interest for decades because of its utilization in numerous modern technical applications. In this article, the results of molecular dynamics simulations are reported to investigate the self-aggregation of sodium dodecyl sulfate (SDS) at an interface of mica and water. SDS molecules starting from lower to higher surface concentrations tend to create distinct aggregated structures in the vicinity of a mica surface. The structural properties, such as density profiles, radial distribution functions, and thermodynamic properties like excess entropy and second virial coefficient, are calculated to address the bits and pieces of the self-aggregation. The change in the free energy for aggregates of varied sizes approaching the surface from the bulk aqueous solution, along with the change in their shapes during the process in terms of change in the radius of gyration and its components, is reported respectively to model a generic pathway for a surfactant-based targeted delivery system.