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This IMA Volume in Mathematics and its Applications GRID GENERATION AND ADAPTIVE ALGORITHMS is based on the proceedings of a workshop with the same title. The work- shop was an integral part of the 1996-97 IMA program on "MATHEMAT- ICS IN HIGH-PERFORMANCE COMPUTING. " I would like to thank Marshall Bern (Xerox, Palo Alto Research Cen- ter), Joseph E. Flaherty (Department of Computer Science, Rensselaer Polytechnic Institute), and Mitchell Luskin (School of Mathematics, Uni- versity of Minnesota), for their excellent work as organizers of the meeting and for editing the proceedings. I also...