one has to search for algo­ rithms that most efficiently and accurately solve systems of 1000, 10,000, or even one million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretisation of partial differential equations. In this case, the matrices are sparse (i. e. , they contain mostly zeros) and well-suited to iterative algorithms. Because of the background in partial differential equa­ tions, this book is closely connected with the author's Theory and Numerical Treatment of Elliptic Differential Equations, whose English translation has also been published by Springer- Verlag. This book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics.