This book has developed from lectures that the author gave for mathematics students at the Ruhr-Universitat Bochum and the Christian-Albrechts-Uni- versitat Kiel. This edition is the result of the translation and correction of the German edition entitled Theone und Numenk elliptischer Differential- gleichungen. The present work is restricted to the theory of partial differential equa- tions of elliptic type, which otherwise tends to be given a treatment which is either too superficial or too extensive. The following sketch shows what the problems are for elliptic differential equations. A:...