  We classify non symplectic prime order automorphisms and all finite order
symplectic automorphism groups of generalised Kummer fourfolds using lattice
theory and recent results on ample cones and monodromy groups. We study various
geometric realisations of the automorphisms obtained in the classification. In
the case of higher dimensional generalised Kummers, we provide full results for
finite symplectic automorphisms groups and we sketch the classification for
prime order non-symplectic groups.
