Ernst Witt, 1911-1991, was one of the most ingenious mathematicians of this century and has decisively shaped the development of various mathematical fields like algebra, number theory, group theory, combinatorics and Lie theory. Among his most important results are the Witt ring of quadratic forms and the ring of Witt vectors. In this volume a complete collection of Witt's research papers are published together for the first time; it also contains various, so far unpublished, articles, facsimiles and photos. Additional English comments by other authors provide an excellent survey on the further development of these mathematical fields. One of Witt's students, Gunter Harder, contributed an essay on Witt vectors.