title: Graph Rewriting and Copying authors: Erik Barendsen and Sjaak Smetsers Graph rewrite systems play an important role in the implementation of functional programming languages. This paper focusses on the theoretical aspects of graph rewriting. Graph reduction is described in terms of general operations on graphs, leading to a substitution-like mechanism called graph replacement. Some basic theory on the interaction of these operations is developed. The ordering induced by graph homomorphisms is investigated. Equipped with this ordering, various sets of graphs have nice domain theoretical properties. Moreover, a lazy copying mechanism is added to the notion of graph reduction. This copying concept is analyzed by splitting it into more elementary graph operations, leading to a confluence result. Finally, some ideas are presented on the use of copying in practice.