Four of the five papers published here had their origins in public lectures to mark the centenary of the first series of lectures given in the University of Cambridge for intending teachers. They are printed here for the first time. The fifth paper, by Professor Davies, has been largely re-written for this volume but uses material previously published elsewhere. Each author has been encouraged to express his personal point of view on developments in his particular domain. Three of the authors contributed the parallel papers in Professor Tibbie's 1966 collection.