  Hahn groups endowed with the canonical valuation play a fundamental role in
the classification of valued abelian groups. In this paper we study the group
of valuation (respectively order) preserving automorphisms of a Hahn group $G$.
Under the assumption that $G$ satisfies some lifting property, we prove a
structure theorem decomposing the automorphism group into a semidirect product
of two notable subgroups. We characterise a class of Hahn groups satisfying the
aforementioned lifting property. For some special cases we provide a matrix
description of the automorphism group.
