have been supported by an increasing body of experimental evidence, derived especially from studies of hydrogen isotope effects. The present book presents an attempt to summarize this evidence and to indicate the main lines of the basic theory. Details of mathematical manipu­ lation are restricted mainly to Chapter 2 and the Appendices, and many readers may prefer to confine themselves to the results obtained. The main emphasis has been on the kinetics of chemical reactions involving the transfer of protons, hydrogen atoms or hydride ions, although Chapter 6 gives an account of the role of the tunnel effect in molecular spectra, and Chapter 7 makes some mention of tunnelling in solid state phenomena, biological processes and the electrolytic discharge of hydrogen. Only passing references have been made to tunnelling by electrons.