Originally published in 1985 this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and--a closely related problem--with the most economical generation of ideals in Noetherian rings. Along the way one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.