In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered:

In the context of Laurent polynomials and Laurent series, the exponents of a monomial may be negative, and in the context of Puiseux series, the exponents may be rational numbers.

In mathematical analysis, it is common to consider polynomials written in terms of a shifted variable ${\displaystyle {\bar {x}}=x-c}$ for some constant ${\displaystyle c}$ rather than a variable ${\displaystyle x}$ alone, as in the study of Taylor series. By a slight abuse of notation, monomials of shifted variables, for instance ${\displaystyle 2{\bar {x}}^{3}=2(x-c)^{3},}$ may be called monomials in the sense of shifted monomials or centered monomials, where ${\displaystyle c}$ is the center or ${\displaystyle -c}$ is the shift.

Since the word "monomial", as well as the word "polynomial", comes from the late Latin word "binomium" (binomial), by changing the prefix "bi-" (two in Latin), a monomial should theoretically be called a "mononomial". "Monomial" is a syncope by haplology of "mononomial".

With either definition, the set of monomials is a subset of all polynomials that is closed under multiplication.

Both uses of this notion can be found, and in many cases the distinction is simply ignored, see for instance examples for the first and second meaning. In informal discussions the distinction is seldom important, and tendency is towards the broader second meaning. When studying the structure of polynomials however, one often definitely needs a notion with the first meaning. This is for instance the case when considering a monomial basis of a polynomial ring, or a monomial ordering of that basis. An argument in favor of the first meaning is that no obvious other notion is available to designate these values,^{[citation needed]} though primitive monomial is in use and does make the absence of constants clear.

The remainder of this article assumes the first meaning of "monomial".

The most obvious fact about monomials (first meaning) is that any polynomial is a linear combination of them, so they form a basis of the vector space of all polynomials, called the monomial basis - a fact of constant implicit use in mathematics.