In publishing this English edition I have tried to make a rather extensive revision. Most of the mistakes and insufficiencies in the original edition have, I hope, been corrected, and some theorems have been improved. Some topics have been added in the form of Appendices to individual sections. Only Appendices A, B and C are from the original. The final section, §33, of the original edition was entitled ‘Kunz’ Theorems' and did not substantially differ from a section in the second edition of my previous book Commutative Algebra (Benjamin, 2nd edn 1980), so I have replaced it by the present §33. The bibliography at the end of the book has been considerably enlarged, although it is obviously impossible to do justice, to all of the ever-increasing literature.

Dr Miles Reid has done excellent work of translation. He also pointed out some errors and proposed some improvements. Through his efforts this new edition has become, I believe, more readable than the original. To him, and to the staff of Cambridge University Press and Kyoritsu Shuppan Co., Tokyo, who cooperated to make the publication of this English edition possible, I express here my heartfelt gratitude.