  We study irreducible modules for map Heisenberg-Virasoro algebras. In
particular, we give a complete classification of irreducible Harish-Chandra
modules for map Heisenberg-Virasoro algebras. We will also classify non-weight
irreducible modules for map Heisenberg-Virasoro algebras whose restriction on
the degree zero part of the universal enveloping algebra of Witt algebra is
free of rank 1.
