This memorial volume is dedicated to E. B. Christoffel on the occasion of the 150th anniversary of his birth. Its aim is, on the one hand, to present the life of Christoffel and the scientific milieu in which he worked and, on the other hand, to present a survey of his work not only in its historical context but especially in the frame of contemporary mathematics and physics. For one thing, this book contains expanded versions of the twelve invited lectures given at the International Christoffel Symposium, held on November 8- 11, 1979 at Aachen and Monschau. For another, the scope of these papers has been broadened by soliciting some fourty-five additional invited articles, concerned either with further aspects of the work of Christoffel or with specia lized topics in fields in which Christoffel had worked. This should give the reader a greater opportunity to appreciate the richness of Christoffel's contributions to the mathematical and physical sciences, and not only its immediate impact but also its subsequent infiuence. It can be discerned that Christoffel did basic work not only in differential geometry or, better still, in classical tensor analysis, thereby supplying the mathematical foundations of Einstein's theory of general relativity, but also in a variety of other areas of mathematics. The scope of Christoffel's work can be appreciated from the following synopsis of the thirteen chapters into which the festschrift is divided. Chap."