A lexeme is an abstract unit of morphological analysis in linguistics, that roughly corresponds to a set of forms taken by a single word. For example, in the English language, run, runs, ran and running are forms of the same lexeme, conventionally written as RUN. A related concept is the lemma (or citation form), which is a particular form of a lexeme that is chosen by convention to represent a canonical form of a lexeme. Lemmas are used in dictionaries as the headwords, and other forms of a lexeme are often listed later in the entry if they are unusual in some way.
A lexeme belongs to a particular syntactic category, has a certain meaning (semantic value), and in inflecting languages, has a corresponding inflectional paradigm; that is, a lexeme in many languages will have many different forms. For example, the lexeme RUN has a present third person singular form runs, a present non-third-person-singular form run (which also functions as the past participle and non-finite form), a past form ran, and a present participle running. (It does not include runner, runners, runnable, etc.) The use of the forms of a lexeme is governed by rules of grammar; in the case of English verbs such as RUN, these include subject-verb agreement and compound tense rules, which determine which form of a verb can be used in a given sentence.
A lexicon consists of lexemes.
The notion of a lexeme is very central to morphology, and thus, many other notions can be defined in terms of it. For example, the difference between inflection and derivation can be stated in terms of lexemes:
The compound root morpheme + derivational morphemes is often called the stem. The decomposition stem + desinence can then be used to study inflection.