This paper presents systematic calculations of the dielectronic recombination (DR) rate coefficient for all energy levels in the ground configuration of each $L$-shell argon ion, Li-like Ar${}^{15+}$ to Ne-like Ar${}^{8+}$. The DR rate coefficients from H-like Ar${}^{17+}$ and He-like Ar${}^{16+}$ are also calculated. The rate coefficients are calculated ab initio using the fully relativistic, parametric potential atomic structure code RELAC. Autoionization rates are computed in the distorted wave approximation using RELAC's wave functions. Configuration interaction (CI) in the levels of the initial and recombined ion is taken into account; CI strongly affects the energies of levels close to the continuum and strongly enhances the rates of weak autoionizing transitions. The contributions to recombination from the promotion of an $n$=1 $(K$ shell) or an $n$=2 $(L$ shell) electron are calculated. Capture of a free electron into levels with principal quantum numbers as high as $n$=14 is allowed, and is extended to $n$=18 in the case of Li- and Be-like ions. The contribution to recombination through high angular momentum orbitals $(l<~6)$ is included in the calculations.