This volume presents the contributions to the international workshop entitled "Lattice Gauge Theory - a Challenge in Large Scale Computing" that was held in Wuppertal from November 4 to 7, 1985. This meeting was the third in a series of European workshops in this rapidly developing field. The meeting intended to bring together both active university research ers in this field and scientists from industry and research centers who pursue large scale computing projects on problems within lattice gauge theory. These problems are extremely demanding from the point of view of both machine hardware and algorithms, for the verification of the continuum fields theories like Quantum Chromodynamics in four-dimensional Euclidean space-time is quite cumbersome due to the tremendously large number of de grees of freedom. Yet the motivation of theoretical physicists to exploit computers as tools for the simulation of complex systems such as gauge field theories has grown considerably during the past years. In fact, quite a few prominent colleagues of ours have even gone into machine building, both in industry and research institutions: more parallelism, and more de dicated computer architecture are their design goals to help them boost the Megaflop rate in their simulation processes. The workshop contained several interesting seminars with status reports on such supercomputer projects like the Italian APE (by E. Marinari), the IBM project GF-11 (by D. Weingarten), and the Danish projects MOSES and PALLAS (by H. Bohr).

Work on the unification of the fundamental particle interac tions has continued vigorously since the first Europhysics study Conference on this subject. At that time we emphasized the exis tence of two main approaches, one based on supersymmetry and pos sibly its local version, supergravity, and the other approach based on grand unified gauge theories. Discussion of the possible tests of these theoretical speculations included experiments on baryon decay and neutrino oscillations. In view of the uncertainties surrounding the observability of such phenomena, the early Universe was welcomed as a possible Laboratory for testing new theoretical ideas. At that time, we expressed the hope that the different gauge and super symmetry approaches would cross-fertilize each other" and it is appropriate to ask now how much of that hope has been realized. We believe there has recently been considerable theoretical rapprochement, which is amply reflected in these Proceedings. On the one hand it has been realized that many of the technical pro blems in grand unified gauge theories, such as arranging the hierarchy of different mass scales, may be alleviated using simple global supersymmetry. On the other hand there has been growing interest in the possibility that extended supergravity theories may furnish a suitable framework for the unification of all the fundamental particle interactions. Many physicists in fact now question actively whether the known "fundamental" particles are in deed elementary, or whether they are composite.

The ASI Quarks, Leptons and Beyond, held in Munich from the 5th to the 16th of September 1983 was dedicated to the study of what we now believe are the fundamental building blocks of nature: quarks and leptons. The subject was approached on two levels. On the one hand, a thorough discussion was given of the status of our knowledge of quarks and leptons and their interactions, both from an experi mental and a theoretical standpoint. On the other hand, open problems presented by the so called standard model of quark and lepton interact ions were explored along various ways that lead one beyond this frame work. One of the principal predictions of the standard model is that weak interactions are mediated by heavy Wand Z vector bosons. These particles were discovered in 1983 at CERN and their relevant proper ties were discussed at the ASI by C. Rubbia. Further theoretical predictions concerning these Z and W bosons, yet to be checked by future experimentation, were discussed by G. Altarelli with a view of seeing where the standard model might fail and new physics ensue. The strong interactions of quarks, based on Quantum Chromodynamics (QeD), are presumed to cause the quarks to bind into hadrons. Pro gress in attempts to calculate the observed hadronic spectrum, ab initio, starting from QCD and employing lattice methods were reviewed at the ASI by P. Hasenfratz.

From 5 to 15 August 1984, a group of 79 physicists from 61 laboratories in 26 countries met in Erice for the 22nd Course of the International School of Subnuclear Physics. The countries represented were Austria, Belgium, Brazil, Bulgaria, Canada, People's Republic of China, Denmark, the Federal Republic of Germany, France, Greece, Hungary, Iran, Israel, Italy, Japan, Korea, Malaysia, Mexico, the Netherlands, Pakistan, Poland, Sweden, Switzerland, Turkey, the United Kingdom, the United States of America. The School was sponsored by the Italian Ministry of Public Education (MPI), the Italian Ministry of Scientific and Technologi cal Research (MRST), the Regional Sicilian Government (ERS), and the Weizmann Institute of Science. The programme of the School was devoted to a review of the most significant results in theoretical and experimental research work on the interactions between what we believe today are the point like constituents of the world: quarks and leptons. It should however not be forgotten that many problems are still to be understood: especially in the forefront of the correla tion between quarks and leptons. This game started in 1966 with the proposal for "leptonic quarks" and went on with "preons" and "rishons" just to quote the most famous attempts to unify these two worlds.