The papers in this volume were presented at an International Symposium on Optimal Estimation in Approximation Theory which was held in Freudenstadt, Federal Republic of Germany, September 27-29, 1976. The symposium was sponsored by the IBM World Trade Europe/Middle East/Africa Corporation, Paris, and IBM Germany. On behalf of all the participants we wish to express our appreciation to the spon- sors for their generous support. In the past few years the quantification of the notion of com- plexity for various important computational procedures (e. g. multi- plication of numbers or matrices)...