The four-volume set LNCS 3036, LNCS 3037, LNCS 3038 and LNCS 3039 constitutes the refereed proceedings of the 4th International Conference on Computational Science, ICCS 2004, held in Krakow, Poland in June 2004.The four volumes present more than 550 reviewed contributed and invited papers of the main conference and its 30 workshops. The papers span the whole range of computational science, from foundational and methodological issues in computer science and algorithmic mathematics to advanced applications in virtually all sciences making use of computational techniques. The proceedings is a unique record of recent progress in the field.