In recent years meshless/meshfree methods have gained a considerable attention in engineering and applied mathematics. The variety of problems that are now being addressed by these techniques continues to expand and the quality of the results obtained demonstrates the effectiveness of many of the methods currently available. The book presents a significant sample of the state of the art in the field with methods that have reached a certain level of maturity while also addressing many open issues. The book collects extended original contributions presented at the first ECCOMAS Conference on Meshless Methods held in 2005 in Lisbon. The list of contributors reveals a mix of highly distinguished authors as well as quite young but very active and promising researchers thus giving the reader an interesting and updated view of different mesh reduction methods and its range of applications. The material presented is appropriate for researchers engineers physicists applied mathematicians and graduate students interested in this active research area.