  The aim of the present paper is the investigation of $Spin(9)$-structures on
16-dimensional manifolds from the point of view of topology as well as holonomy
theory. First we construct several examples. Then we study the necessary
topological conditions resulting from the existence of a $Spin(9)$-reduction of
the frame bundle of a 16-dimensional compact manifold (Stiefel-Whitney and
Pontrjagin classes). We compute the homotopy groups $\pi_i (X^{84})$ of the
space $X^{84}= SO(16) / Spin(9)$ for $i \le 14$. Next we introduce different
geometric types of $Spin(9)$-structures and derive the corresponding
differential equation for the unique self-dual 8-form $\Omega^8$ assigned to
any type of $Spin(9)$-structure. Finally we construct the twistor space of a
16-dimensional manifold with $Spin(9)$-structure and study the integrability
conditions for its universal almost complex structure as well as the structure
of the holomorphic normal bundle.
