All-atom molecular dynamics simulation results regarding aqueous sodium dodecyl sulfate (SDS) solutions have been presented. Both salt-free solutions with different SDS concentrations and those containing calcium chloride additives have been studied. The simulation has shown that surface-active SDS ions form stable premicellar aggregates. The obtained molecular dynamics trajectories have been used to describe both the kinetic and structural properties of solutions containing SDS molecular aggregates and the properties of individual aggregates. Aggregation kinetics has been investigated, and the characteristic sizes of the aggregates have been calculated by different methods. It has been found that the size of a premicellar aggregate with aggregation number n = 16 in a salt-free solution virtually does not depend on surfactant concentration. Radial distribution functions (RDFs) of hydrogen and oxygen atoms of water molecules relative to the center of mass of an aggregate have no local maxima near the aggregate