This is a sequel to the book “Programming the Boundary Element Method” by G. Beerpublished by Wiley in 2001. The scope of this book is different however and this is reflected in the title. Whereas the previous book concentrated on explaining the implementation of a limited range of problems into computer code and the emphasis was on programming, in the current book the problems covered are xtended, the emphasis is on explaining the theory and computer code is not presented for all topics. The new topics covered range from dynamics to piezo-electricity. However, the main idea, to provide an explanation of the Boundary Element Method (BEM), that is easy for engineers and scientists to follow, is retained. This is achieved by explaining some aspects of the method in an engineering rather than mathematical way. Another new feature of the book is that it deals with the implementation of the method on parallel processing hardware. I. M. Smith, who has been involved in programming the finite element method for decades, illustrates that the BEM is “embarrassingly parallelisable”. It is shown that the conversion of the BEM programs to run efficiently on parallel processing hardware is not too difficult and the results are very impressive, such as solving a 20 000 element problem during a “coffee break”. Due to the fact that, compared to the Finite Element Method, a significantly smaller group of people are working in this field the development of the method is lagging considerably behind. The often quoted comparison that the method is a “Cinderella”, dominated by her “big sister”, the Finite Element Method, and whose beauty is hidden away, is still true and we hope that the reader will see the beauty of the method in the examples on industrial applications and the advanced topics presented at the end. The book includes some innovative development work carried out by the small but very active group at the Institute for Structural Analysis, Graz University of Technology, Austria under the leadership of G. Beer. The main scope of their research is to further develop the method, so that it can be applied to a much wider range of practical problems in engineering, one particular application of interest being in the field of geotechnical engineering, especially underground excavation. programming, in the current book the problems covered are xtended, the emphasis is on explaining the theory and computer code is not presented for all topics. The new topics covered range from dynamics to piezo-electricity. However, the main idea, to provide an explanation of the Boundary Element Method (BEM), that is easy for engineers and scientists to follow, is retained. This is achieved by explaining some aspects of the method in an engineering rather than mathematical way. Another new feature of the book is that it deals with the implementation of the method on parallel processing hardware. I. M. Smith, who has been involved in programming the finite element method for decades, illustrates that the BEM is “embarrassingly parallelisable”. It is shown that the conversion of the BEM programs to run efficiently on parallel processing hardware is not too difficult and the results are very impressive, such as solving a 20 000 element problem during a “coffee break”. Due to the fact that, compared to the Finite Element Method, a significantly smaller group of people are working in this field the development of the method is lagging considerably behind. The often quoted comparison that the method is a “Cinderella”, dominated by her “big sister”, the Finite Element Method, and whose beauty is hidden away, is still true and we hope that the reader will see the beauty of the method in the examples on industrial applications and the advanced topics presented at the end. The book includes some innovative development work carried out by the small but very active group at the Institute for Structural Analysis, Graz University of Technology, Austria under the leadership of G. Beer. The main scope of their research is to further develop the method, so that it can be applied to a much wider range of practical problems in engineering, one particular application of interest being in the field of geotechnical engineering, especially underground excavation.