An enumeration of a collection of items is a complete, ordered listing of all of the items in that collection. The term is commonly used in mathematics and theoretical computer science, to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to contain repetitions) depend on the branch of mathematics and the context in which one is working.

Some sets can be enumerated by means of a natural ordering (such as 1, 2, 3, 4, ... for the set of positive integers), but in other cases it may be necessary to impose a (perhaps arbitrary) ordering. In some contexts, such as enumerative combinatorics, the term enumeration is used more in the sense of counting – with emphasis on determination of the number of elements that a set contains, rather than the production of an explicit listing of those elements.

In combinatorics, enumeration means counting, i.e., determining the exact number of elements of finite sets, usually grouped into infinite families, such as the family of sets each consisting of all permutations of some finite set. There are flourishing subareas in many branches of mathematics concerned with enumerating in this sense objects of special kinds. For instance, in partition enumeration and graph enumeration the objective is to count partitions or graphs that meet certain conditions.