the area of graph grammars is theoretically attractive and well motivated byvarious applications. more than 20 years ago, the concept of graph grammars was introduced by a. rosenfeld as a formulation of some problems in pattern recognition and image processing, as well as by h.j. schneider as a method for data type specification. within graph-grammar theory one maydistinguish the set-theoretical approach, the algebraic approach, and the logical approach. these approaches differ in the method in which graph replacement is described. specific approaches, node replacement and hyperedge replacement, concern the basic units of a hypergraph, nodes and hyperedges. this monograph is mainly concerned with the hyperedge-replacement approach. hyperedge-replacement grammars are introduced as a device for generating hypergraph languages including graph languages and string languages. the concept combines a context-free rewriting with a comparatively large generative power. the volume includes a foreword by h. ehrig.