This section includes tutorials showing how to do basic commutative algebra constructions in Macaulay2. This section is being written by Mike Stillman, for use with his Fall 2005 course: Math 634, Commutative algebra, at Cornell University. This course covers basic commutative algebra, at the level of Atiyah-Macdonald, and Greuel-Pfister.
Macaulay2 examples corresponding to the Singular examples in the book by Greuel-Pfister may also be found here.