These papers were presented at the workshop on High Performance Computing and Gigabit Wide Area Networks held in September 1998 in Essen, Germany. The aim of the workshop was to analyse the interplay between computer network technology, communication software and the performance of mathematical algorithms used for large scale computations in wide area high speed computer networks. Only through interdisciplinary research with the co-operation of electrical engineers, mathematicians and computer scientists will it be possible to determine the most efficient combinations of parallel algorithms, protocols and network hardware. This workshop brought together scientists working in computer networks, network protocols and numerical and linear algebra and new insights were gained that have previously been unattainable. This volume contains 22 refereed research articles that reflect the exciting new developments in this field.