All polynomials in Macaulay are stored as an ordered list of monomials. The order on monomials is a parameter for standard bases which can be modified. Different applications of standard bases often require different monomial orders. Macaulay is flexible enough to allow the user to define arbitrary monomial orders. This order is defined using the ring command.
The most important monomial orders are the reverse lexicographic order, product orders and elimination orders. Almost every application involving standard (Gröbner) bases uses only these orders. On the first reading, most users should skip the section on general monomial orders.