The PARA workshops in the past have been devoted to parallel computing methods in science and technology. There have been seven PARA meetings to date: PARA'94, PARA'95 and PARA'96 in Lyngby, Denmark, PARA'98 in Umeå, Sweden, PARA'2000 in Bergen, Norway, PARA'02 in Espoo, Finland, and PARA'04 again in Lyngby, Denmark. The rst six meetings featured lectures in modern numerical algorithms, computer science, engineering, and industrial applications, all in the context of scientific parallel computing. This meeting in the series, the PARA'04 Workshop with the title State of the Art in Scientific Computing , was held in Lyngby, Denmark, June 20-23, 2004. The PARA'04 Workshop was organized by Jack Dongarra from the University of Tennessee and Oak Ridge National Laboratory, and Kaj Madsen and Jerzy Wasniewski from the Technical University of Denmark. The emphasis here was shifted to High-Performance Computing (HPC). The ongoing development of ever more advanced computers provides the potential for solving increasingly dif cult computational problems. However, given the complexity of modern computer architectures, the task of realizing this potential needs careful attention. For example, the failure to exploit a computer's memory hierarchy can degrade performance badly. A main concern of HPC is the development of software that optimizes the performance of a given computer. The high cost of state-of-the-art computers can be prohibitive for many workplaces, especially if there is only an occasional need for HPC. A solution to this problem can be network computing, where remote computing facilities are exploited via the internet. PARA'04 featured invited talks, contributed talks, minisymposia, and software and hardware vendors. The rst day, June 20, was devoted to two parallel tutorials. The minisymposia and contributed talks during the main part of the Workshop, June 21-23, were scheduled in parallel sessions. All invited and contributed talks were noncommercial. The Workshop attracted 230 speakers from all over the world. The PARA'06 Workshop with the title State-of-the-Art in Scienti c and Parallel Computing will be held in Umeå (Sweden) on June 17-21, 2006.