The Appalachian Math Science Partnership (AMSP) is a project within NSF's (National Science Foundation's) Math Science Partnerships (MSP) initiative. Funded at $23 million over five years, the AMSP involved 51 school districts and nine higher education institutions in Kentucky, Tennessee and Virginia. The AMSP faced two significant challenges in its effort to live up to the vision of the MSP initiative and to its own hopes and goals. First, its service area, Appalachia, comprises some of the most isolated and stressed communities and school systems in the United States. Second, the mere scale of the partnership--60 organizations in several states--defied easy implementation. Yet despite these challenges (indeed, working to address them directly), the AMSP built upon existing leadership capacity in the region and created not only effective partnerships, but ultimately formed what is viewed as the foundation for a sustainable regional "improvement infrastructure" for science and mathematics. In this set of five papers, the authors portray the evolution, design and strategies of the AMSP. This paper is the core document of the set of five and stands alone. It provides background on the initiative and on the regional landscape, gives an account of how the AMSP's overall design as an "umbrella partnership" formed, describes the major strategies and components of the partnership (including the benefits they produced and lessons learned from their implementation), documents the core values and design principles underlying the umbrella partnership, and offers the authors' conceptualization of the AMSP as a regional improvement infrastructure. Appendices include: (1) NSF-Funded Projects in Appalachia Prior to or Active During the AMSP; and (2) AMSP Research Activities Conducted by Inverness Research. (Contains 17 footnotes and 2 figures.) ["The Appalachian Math Science Partnership: A Multi-State Umbrella Partnership Promoting Local Mathematics and Science Reform" was written with Mike Howard, Laura Stokes and Dawn Robles. For the accompanying report, see ED508681.]