This book constitutes the thoroughly refereed post-proceedings of the First European Across Grids Conference held in Santiago de Compostela, Spain in February 2003. The 39 revised full papers presented were carefully selected during two rounds of reviewing and improvement. The papers address all current issues in grid computing, in particular grid middleware architectures, tools, resource management, job scheduling, data management, grid-based distant e-learning, stream-oriented database management, data stripping, large-scale grid applications, simulation, visualization, data mining, grid performance analysis, and grid monitoring.