The course deals with the numerical solution of boundary value problems by boundary element methods (BEM). Weighted residual techniques, the reciprocity theorem and transformation on the boundary using fundamental solutions from the basic concept of the method. Following, the numerical implementation of BEM is covered: geometry discretization, numerical integration and field point evaluation. Application to problems in potential theory (heat conduction), acoustics and elastomechanics including structure-borne sound propagation are presented. An outlook on advanced topics like hybrid BEM, Dual Reciprocity BEM and BEM-FEM coupling is given.