  In this paper we deal with monogenic and $k$-hypermonogenic automorphic forms
on arithmetic subgroups of the Ahlfors-Vahlen group. Monogenic automorphic
forms are exactly the 0-hypermonogenic automorphic forms. In the first part we
establish an explicit relation between $k$-hypermonogenic automorphic forms and
Maa{\ss} wave forms. In particular, we show how one can construct from any
arbitrary non-vanishing monogenic automorphic form a Clifford algebra valued
Maa{\ss} wave form.
  In the second part of the paper we compute the Fourier expansion of the
$k$-hypermonogenic Eisenstein series which provide us with the simplest
non-vanishing examples of $k$-hypermonogenic automorphic forms.
