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Let $E$ be the fundamental group of a closed Sol 3-manifold. We describe thegroups $Aut(E)$ and $Out(E)$. We first consider the case where $E$ is thefundamental group of a torus bundle, and then the case where $E$ is thefundamental group of a closed Sol 3-manifold which is not a torus bundle. Thegroups are described in terms of some iterated semi-direct products of wellknown groups, where one exception is for $Out(E)$ for some $E$'s, in which case$Out(E)$ is described as an extension and a presentation is given.

The group Aut and Out of the fundamental group of a closed Sol 3-manifold