Over the past years meshfree methods for the solution of partial di?erential equations have signi?cantly matured and are used in various ?elds of appli- tions. One of the reasons for this development is the fact that meshfree d- cretizationsandparticlemodels areoftenbetter suitedto copewithgeometric changes of the domain of interest than mesh-based discretization techniques such as ?nite di?erences, ?nite elements or ?nite volumes. Furthermore, the computational costs associated with mesh generation are eliminated in me- free approaches, since they are based only on a set of independent points. From the modelling point of view, meshfree methods gained much interest in recent years since they may provide an e?cient and reliable approach to the coupling of contiuum models to particle models. In light of these developments the Sonderforschungsbereich 611 and the Gesellschaft fur Mathematik und Mechanik sponsored the second interna- .. tionalworkshoponMeshfreeMethodsforPartialDi?erentialEquations.Itwas hostedby the Institut fur .. Numerische Simulationatthe Rheinische Friedrich- Wilhelms Universit. at Bonn from September 15 to September 17, 2003. The organizers Ivo Babu? ska, Ted Belytschko, Michael Griebel, Wing Kam Liu, Helmut Neunzert, and Harry Yserentant invited scientist from twelve co- tries to Bonn with the aim to bring together European, American and Asian researchers working in this exciting area of interdisciplinary research. The objective of the workshop was not only to strengthen the mathematical - derstanding and analysis of meshfree discretizations but also to promote the exchange of ideas on their implementation and application.