The Fourth International Workshop on Meshfree Methods for Partial D- ferential Equations was held from September 17 to September 20, 2007 in Bonn, Germany. One of the major goals of this workshop series is to bring together European, American and Asian researchers working in this exciting ?eld of interdisciplinary research on a regular basis. To this end Ivo Babu? ska, Ted Belytschko, Michael Griebel, Antonio Huerta, Wing Kam Liu, and Harry Yserentant invited scientist from twelve countries to Bonn to strengthen the mathematical understanding and analysis of meshfree discretizations but also to promote the exchange of ideas on their implementation and application. The workshop was again