The decade since the appearance of the first edition of this book has seen the publication of some important books in commutative algebra, such as D. Eisenbud's ‘Commutative algebra with a view toward algebraic geometry’ [5], which stresses the geometric heritage of the subject, and W. Bruns' and J. Herzog's ‘Cohen–Macaulay rings’ [2], There is therefore even more motivation to encourage young people to study commutative algebra, and so, in my opinion, the raison d'être for this book – to provide ‘stepping stones’ to help young people into the subject so that they can go on to study more advanced books with confidence – is as strong as ever.

This second edition contains two new chapters, namely Chapter 16 on ‘Regular sequences and grade’ and Chapter 17 on ‘Cohen–Macaulay rings’. These chapters are just ideal-theoretic introductions to the topics of their titles: a complete treatment of them would involve significant use of homological algebra, and that is beyond the scope of the book. Nevertheless, there are some ideal-theoretic aspects which can be developed very satisfactorily within the framework of the book, and, indeed, which provide good applications of ideas developed in earlier chapters; it is those aspects which receive attention in these new chapters. It is hoped that they will whet the reader's appetite to explore Bruns' and Herzog's [2], a book which provides ample evidence of the importance of the Cohen–Macaulay condition.

I have taken the opportunity to make a few improvements to, and correct a small number of misprints in, the fifteen chapters which formed the first edition.