The rapid development of numerical analysis as a subject in its own right, as well as its increasing applicability to mathematical modeling in sciences and engineering, have led to a plethora of journals in its various subdisciplines, ranging from Computational Fluid Dynamics to Linear Algebra. These journals obviously represent the frontiers of research in their area. However, each specialization of numerical analysis is intricately linked and a broad knowledge of the subject is necessary for the solution of any "real" problem. Such an overview cannot be successfully achieved through either a single volume or a journal since the subject is constantly evolving and researchers need to be kept continuously informed of recent developments in a wide range of topics. Acta Numerica is an annual publication containing invited survey papers by leading researchers in a number of areas of applied mathematics. The papers included present overviews of recent developments in their area and provide "state of the art" techniques and analysis. Volume 1 aptly represents the flavor of the series and includes papers on such diverse topics as wavelets, optimization, and dynamical systems.