  We give a definition of hypergraph C*-algebras. These generalize the
well-known graph C*-algebras as well as ultragraph C*-algebras. In contrast to
those objects, hypergraph C*-algebras are not always nuclear. We provide a
number of non-nuclear examples, we prove a Gauge-Invariant Uniqueness Theorem
for a subclass of hypergraph C*-algebras and we study moves on hypergraphs
which generalize the moves in the theory of graph C*-algebras.
