This volume represents the proceedings of a NATO Advanced Studies Instituteheld near Barga (Italy), July 11-23, 1988, involving over 90 participants from more than twelve countries of Europe, North America and elsewhere. It was not our intention at this meeting to present a complete up-to-the-minute review of current research in enzyme catalysis but t·ather, in accord wi th the intended spiri t of NATO ASis, to gi ve an opportunity for advanced students and researchers in a wide variety of disciplines to meet tagether and study the problern from different points of view. Hence the lectures cover topics rauging from the purely theoretical aspects of chemical reaction kinetics in condensed matter through practical experimental approaches to enzyme structure, dynamics and mechanism, including the new experimental opportunities arising from genetic engineering techniques. Our approachwas unashamedly physical, both because the more biochemical aspects of enzymology are amply covered elsewhere and because progress in our understanding and application of the molecular basis of enzymic processes must ultimately come from advances in physical knowledge. We tried to cover as wide a spectrum as possible, and succeeded in gathering an expert and enthusiastic team of speakers, but there . are some inevitable omissions. In particular, and with hindsight, our discussions might have been enriched by more detailed coverage of general aspects of chemical catalysis - but readers requiring this background should find adequate references herein.