Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal

This is the English translation (by Michael P. Abramson) of the PhD thesis of Bruno Buchberger, in which he introduced the algorithmic theory of Grobner bases. Some comments by Buchberger on the translation and the thesis are given in an additional short paper in this issue of the Journal of Symbolic Computation. (c) 2005 Published by Elsevier Ltd.