Construct of the form
n=0 anxn
where x is a formal variable and the an are coefficients (usually coming from a field, but sometimes from more exotic objects. Using the standard rules of algebra we can perform formal operations on the series, like addition and multiplication; others may be possible, depending on where we get our coefficients from.

Sometimes we'll use a power series about x0, by replacing "x" above with "(x-x0)" throughout.

In analysis we usually also demand that our power series converge in some neighbourhood.

All Taylor series (and MacLaurin series) are power series.