An approach to high-resolution restriction-fragment DNA mapping, known as Multiple-Restriction-Enzyme mapping (MRE mapping), is present. This approach significantly reduces the uncertainty of clone placement by using clone ends to synchronize the position in of clones within different maps, each map being constructed from fragment-length data produced by digestion of each clone with a specific restriction enzyme. Maps containing both fragments-length data and clone-end data are maintained for each restriction enzyme, and synchronization between two such maps is achieved by requiring them to have "compatible" clone-end map projections. Basic definitions of different kinds of maps, such as restriction sites maps, restriction fragment maps and clone end maps, are presented. Several specifications notations, such as sequence-set notation and sequence-set-tree notation, for describing the structure of these maps, are defined. Basic concepts, such as the match/merge approach to map incorporation, extension vs. assimilation and ambiguity, are exposed. Supporting techniques, such as window sizing, window placement, and ambiguity resolution, are also discussed. A mathematical analysis of how MRE mapping effects false positives and false negatives is presented. For concreteness, MRE mapping is presented using a specific methodological framework. However, many of the concepts and techniques have a wider range of use than just high-resolution restriction-fragment mapping.