This book constitutes the thoroughly refereed post-proceedings of the International Workshop on Membrane Computing, WMC 2003, held in Tarragona, Spain, in July 2003. The 26 revised full papers presented were carefully selected during two rounds of reviewing and improvement. All current topics in the emerging area of membrane computing are addressed, ranging from issues in mathematics and theoretical computer science to (potential) applications in biology, bioinformatics, sorting, ranking, linguistics, and computer graphics; several implementations and simulations on computers, computer networks, and reconfigurable hardware are presented too.