The Conference on Boundary Elements and Mesh Reduction Methods is the recognised international forum for presentation and discussion of the latest advances in these methods and their applications in science and engineering. Since 1978 the conference has produced a series of volumes in which all major developments in the field have been presented. This valuable collection is available in digital form from 1993 in the Wessex Institute eLibrary (http://library.witpress.com) where it can be easily accessed by the international scientific community. The continuous success of the conference since the first meeting took place in 1978 indicates the strength of the research carried out by different groups around the world. The history of the Conference traces the evolution of advanced methods since the first successful development of boundary integral techniques into BEM took place to the recent Mesh Reduction Methods. The objective of the meetings is the further development of technologies that reduce or eliminate the type of meshes required by first generation computational methods such as finite differences and finite elements. The aim is being achieved first through the emergence of BEM as a method that eliminates the need for an internal mesh and more recently through the development of a series of advanced techniques for further mesh reduction, culminating in the emergence of meshless methods.