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This volume contains the papers presented at the Conference on Computational Methods in Band Theory sponsored jointly by IBM and the American Physical Society and held at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York, on May 14-15, 1970. The purpose of the conference was a sharing of information on the computational problems involved in relating models for the electron-electron and electron-ion interactions to experimentally measurable quantities. The papers comprising this volume therefore present up-to-date methodology for the calculation of single-particle energies and wave functions for periodic and near-periodic systems, the integration over these states required to describe experiment, and computationally practicable procedures for the introduction of exchange and correlation and the achievement of self-consistency. The proceedings is actually an expansion of the conference in that, unlike the oral presentations, the papers were not limited as to length. Furthermore, time was allowed after the conference to permit the papers to be written with the conference in retrospect, and five "prepared discussion" papers written by attendees of the conference but not on the original program are included. The latter are indicated in the table of contents by asterisks. The explicit emphasis of the conference on comparison of technique generated much lively argument, which is surely an indi- cation of the current interest in the subject and the vigor of those working in it. It is our hope that the proceedings will make these comparisons available to the widest possible audience.