Lectures given at The Lancaster Numerical Analysis Summer School

Each week of this three week meeting was a self-contained event, although each had the same underlying theme - the effect of parallel processing on numerical analysis. Each week provided the opportunity for intensive study to broaden participants' research interests or deepen their understanding of topics of which they already had some knowledge. There was also the opportunity for continuing individual research in the stimulating environment created by the presence of several experts of international stature. This volume contains lecture notes for most of the major courses of lectures presented at the meeting; they cover topics in parallel algorithms for large sparse linear systems and optimization, an introductory survey of level-index arithmetic and superconvergence in the finite element method.