The results of molecular modeling of ionic surfactant self-aggregation in sodium dodecyl sulphate (SDS) aqueous solutions, both salt-free and with addition of NaCl, are reported. The modeling has been based on all-atom molecular dynamics simulations at several SDS concentrations. Formation of one or three ionic aggregates of different size have been observed in the molecular dynamics runs. The computed trajectories of molecules and ions have been used to study the effects of aggregation on local densities of water molecules and counterions, and on the diffusivitives of the aggregates themselves. With finding the mean force potential, the degree of counterion binding for aggregates with different aggregation numbers has been estimated. The results have been compared with the classical square-gradient density functional computations for a single ionic micelle in polar solvent. In addition, the influence of size of the simulation box on the transport properties of SDS aggregates has been investigated. In particu