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The first edition of this book was based on the lectures which I gave at Cornell University during 1958 as George Fisher Baker Lecturer, and I would like to repeat my warmest thanks to Professor F. A. Long and the other members of the Department of Chemistry for their kindness and helpful advice. The present edition was largely written during the tenure of a Visiting Professorship awarded by the Royal Society and the Israeli Academy of Sciences. I am deeply indebted to both of these bodies and also to the hospitality of the Weizmann Institute of Science, in particular to Professor David Samuel and Professor F. S. Klein of the Isotopes Research Department. The subject as a whole has expanded greatly since 1959, especially in two fields, namely, the direct study of fast proton-transfer reactions (notably by the relaxation methods pioneered by Eigen), and the experi- mental and theoretical study of hydrogen isotope effects. In order to keep the size of the book within reasonable bounds it has been necessary to adopt a selective policy, and this is particularly the case in Chapter 9 where I have chosen to treat a few types of reaction in some detail rather than to attempt a more complete coverage.