The kinetic phenomena in micellar solutions strongly depend on diffusivities of micelles, premicellar aggregates, surfactant monomers, surface active ions, counterions, and coions [1-6]. Even using contemporary experimental equipment and techniques, it is practically impossible to distinguish between the aggregates having different aggregation numbers and, consequently, to study them separately. On the other hand, methods of molecular modeling allow one to investigate transport and structural properties of individual aggregates with arbitrary aggregation numbers in detail. In the presented study we use all-atom molecular dynamics to model the process of micellization in sodium dodecyl sulphate (SDS) aqueous solution starting from the surfactant molecules uniformly distributed in the simulation cell to the formation of small short-lived aggregates and their subsequent fusion into larger quasistable aggregates. The molecular dynamics simulation of SDS aqueous solutions, both salt-free and with added N