In this paper, we address the problem of providing foundations for metadata rnanagement by developing an order to compare the amount of information transferred by schema mappings. From this order we derive several other criteria to compare mappings, we provide tools to deal with these criteria, and we show their usefulness in defining and studying schema mapping operators. More precisely, we show how the machinery developed can be used to study the extract and merge operators, that have been identified as fundamental for the development of a metadata management framework. We also use oar machinery to provide simpler proofs for some fundamental results regarding the inverse operator, and we give an effective characterization for the decidability of the well-known schema evolution problem.