A pulsed discharge light source was used to study the two and three times ionized argon (Ar II, Ar III) spectra in the 480–6218 Å region. A set of 129 transitions of Ar III and 112 transitions of Ar IV were classified for the first time. We extended the analysis of Ar III to five new energy levels belonging to 3s23p34d, 3s23p35s odd configurations. For Ar IV, 10 new energy levels of the 3s23p23d and 3s23p24p even and odd configurations, respectively, are presented. For the prediction of energy levels, line transitions, and transition probabilities, relativistic Hartree–Fock calculations were used.