The International Workshops on "The Use of Supercomputers in Theoretical Science" have become a tradition at the Univer­ sity of Antwerp, Belgium. The first one took place in 1984. This volume combines the proceedings of the second work­ shop (December 12, 1985), of the third (June 16, 1987) and of the fourth (June 9, 1988). The principal aim of the International Workshops is to present the state-of-the-art in scientific high speed computa­ tion. Indeed, during the past ten years computational science has become a third methodology with merits equal to the theo­ retical and experimental sciences. Regretfully, access to supercomputers remains limited for academic researchers. None­ theless, supercomputers have become a major tool for scientists in a wide variety of scientific fields, and they lead to a realistic solution of problems that could not be solved a decade ago. It is a pleasure to thank the Belgian National Science Foundation (NFWO-FNRS) for the sponsoring of all the workshops. These workshops are organized in the framework of the Third Cy­ cle "Vectorization, Parallel Processing and Supercomputers", which is also funded by the NFWO-FNRS. The other sponsor I want to thank is the University of Antwerp, where the workshops took place. The University of Antwerp (UIA), together with the NFWO-FNRS, are also the main sponsors of the ALPHA-project, which gives the scientists of Belgium the opportunity to obtain an easy supercomputer connection.