  Let $L/F$ be a Galois extension of fields with Galois group isomorphic to the
quaternion group of order $ 8 $. We describe all of the Hopf-Galois structures
admitted by $ L/F $, and determine which of the Hopf algebras that appear are
isomorphic as Hopf algebras. In the case that $ F $ has characteristic zero we
also determine which of these Hopf algebras are isomorphic as $ F $-algebras
and explicitly compute their Wedderburn-Artin decompositions.
