Titel: Hypersymplectic Geometry Gauge Theory Abstract: Hypersymplectic manifolds are split-signature analogues of hyperkähler manifolds. In this talk we will start by defining hypersymplectic structures and discussing some of their properties. In particular, we will describe the hypersymplectic quotient construction due to Hitchin, which is the hypersymplectic version of the Marsden-Weinstein symplectic reduction. In the second part of the talk we will illustrate these ideas by studying a gauge-theoretic example.