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Today many application engineers struggle to not only publish their relational, object or ascii file data on the Web but to also integrate information from diverse sources, often inventing and reinventing a suite of hard-wired integration tools. A model management system that supports the specification and manipulation of not only data models and schemata, but also mappings between the different models in a generic manner has the promise of solving these issues. However, support for modeling and managing such mappings as objects remains an unsolved challenge. In our work, we propose a powerful middleware tool that successfully tackles this challenge. For this, we propose a graph-theoretic framework that allows users to explicitly model mappings between different data models as well as re-structuring within one data model. Our map metamodel is based on a set of re-usable mapping constructs that can in principle be applied on any data model described in our framework. In our work, we have tested these operators for XML and relational model mappings. Using the description of maps at the model level, mappings between specific application schemas and transformations of associated application data can be automated by our framework. Our framework guarantees the correctness of the map, of the generated transformation code, of the output data model, and of the generated application schemas, based on the correctness criteria for the map metamodel. In this paper, we also introduce the model management system Gangam that we are developing to realize our proposed map modeling theory. With Gangam we show not only the feasibility of our approach but also demonstrate the re-usability and the ease of end-to-end development of modeling strategies. To further illustrate our ideas, we present a walk-through example of mapping an application DTD to a relational application schema using Gangam.