This book contains 18 scientific papers setting out the latest developments in the scientific disciplines and endeavours to which Professor P. G. Burke has contributed over the last 40 years, prior to his formal retirement in September 1998. The aim of the volume is to provide an up-to-date survey of the latest developments in many areas of atomic and molecular collision physics and applications and also a number of scientific disciplines where supercomputers play a central role. It will be of use to researchers in various scientific areas and especially to those entering new areas of atomic, molecular and optical physics. The book will form a permanent record celebrating the many contributions by Professor P. G. Burke, CBE, FRS, to the advancement of scientific knowledge.