The concentration dependence of viscosity of an electrolyte solution has remained largely an ill-understood problem of solution chemistry. Here we present a microscopic study of the problem aimed at removing this lacuna. A new microscopic expression for the ionic contribution to the viscosity of an electrolyte solution has been derived which expresses it in terms of the static and dynamic structure factors of the charge and the number densities of the electrolyte solution. This ionic contribution becomes the excess viscosity for extremely dilute solutions. The celebrated expression of Falkenhagen follows exactly from the microscopic expression in the limit of very low ion concentration. The present theory is a self-consistent theory which also includes the concentration dependence of the electrolyte friction on the ions. Numerical results reveal that the viscosity of a solution at finite concentration can be very different from that given by the Falkenhagen expression. The present theory predicts a stronger increase of viscosity with increase of ion concentration, especially for ions of higher valence which is in qualitative agreement with experimental results. The theory suggests that, for viscosity, the molecular nature of the ion-solvent interactions could be important even at very low ion concentration.