Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra, developed with funding from the National Science Foundation. We are eager to help new users get started with it.

This documentation describes version **1.21** of Macaulay2.

The object Macaulay2Doc is a package.

- rings
- ideals
- matrices
- substitution and maps between rings
- modules
- chain complexes
- varieties
- Gröbner bases

- normal forms
- elimination of variables
- IntegralClosure -- routines for integral closure of affine domains and ideals
- primaryDecomposition -- irredundant primary decomposition of an ideal
- combinatorial functions

- changes to Macaulay2, by version
- mathematical examples
- basic commutative algebra
- replacements for commands and scripts from Macaulay
- how Macaulay2 finds its files