Having run out of hard copies of the book a number of years ago, the author is pleased to publish an on-line version of the book in PDF format. A number of minor corrections have been made to the original, following feedback from a number of readers. The author is particularly grateful to Ambrose Thompson and Peter Juhl for their feedback.There have obviously been a number of advances since the publication of the first print in 199S. The author has created the website www.houndary-element-method.com as a general resource on the method. Further developments and applications of the work can be found in the Addendum at the back of this book or on the webpage www.boundary-element-method.com/extra.