The numerical treatment of integral equations is an important problem in science and industry. Regardless of whether the integral equation is a straight model of a physical state, like the radiosity or the heat radiation equation, or whether it is derived from partial differential equations, a memory and computing time efficient solving algorithm is essential for all practical applications. The present book is dedicated to the fast solution of boundary integral equations on unstructured meshes by the Galerkin scheme and its application to the special situation of the radiosity equation. Throughout the pages a new fast method based on the wavelet compression and the ideas of the hierarchical matrices will be constructed. To allow for comfortable comprehension, the author describes in detail all used methods and algorithms including the wavelet method as well as the H²-matrices. Although this book is primarily written for applied mathematicians, its detailed descriptions also provide a good introduction to the field of fast boundary element methods for computer scientists and engineers.