Symmetry plays an important role in theoretical physics‎,‎ applied analysis‎,‎ classical differential equations‎,‎ and bifurcation theory‎.‎ Although numerical analysis has incorporated aspects of symmetry on an ad hoc basis‎,‎ there is now a growing collection of numerical analysts who are currently attempting to use symmetry groups and representation theory as fundamental tools in their work‎.‎ This book contains the proceedings of an AMS‎-SIAM Summer Seminar in Applied Mathematics‎,‎ held in 1992 at Colorado State University‎.‎ The seminar‎,‎ which drew about 100 scientists from around the world‎,‎ was intended to stimulate the systematic incorporation of symmetry and group theoretical concepts into numerical methods‎.‎ The papers in this volume have been refereed and will not be published elsewhere‎.‎