This book constitutes the thoroughly refereed post-proceedings of the First International Workshop on Approximation and Online Algorithms, WAOA 2003, held in Budapest, Hungary in September 2003.The 19 revised full papers presented together with 5 invited abstracts of the related ARACNE mini-symposium were carefully selected from 41 submissions during two rounds of reviewing and improvement. Among the topics addressed are competitive analysis, inapproximability results, randomization techniques, approximation classes, scheduling, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and applications to game theory and financial problems.