Macaulay2 differs from other computer algebra systems such as Maple and Mathematica, in that before making a polynomial, you must create a ring to contain it, deciding first the complete list of indeterminates and the type of coefficients permitted. Recall that a ring is a set with addition and multiplication operations satisfying familiar axioms, such as the distributive rule. Examples include the ring of integers (ZZ), the ring of rational numbers (QQ), and the most important rings in Macaulay2, polynomial rings.

The sections below describe the types of rings available and how to use them.

For additional common operations and a comprehensive list of all routines in Macaulay2 which return or use rings, see Ring.

- basic rings of numbers
- integers modulo a prime
- finite fields
- polynomial rings
- monoid -- make or retrieve a monoid
- monomial orderings
- graded and multigraded polynomial rings
- quotient rings
- manipulating polynomials
- factoring polynomials