In order to describe the form of the linguistic expressions (phrases, sentences, texts) in a language, we must describe how those complex expressions are built from smaller parts, until ultimately we which the atoms of linguistic form. The term morpheme is used to refer to an atom of linguistic form.
Most languages have a word like the English word 'word', that appears at first to refer to precisely the sorts of minimal linguistic objects we have in mind. But there are two reasons to reject 'word' as the label for the minimal unit of linguistic form:
The term 'word' is ambiguous, referring to at least three different sorts of object. In many languages, linguistic expressions we would want to identify as words are in fact structurally complex. We consider the second of these points here; the first is taken up below.
The following are all words of English:
cat cats cat+s
help helped help+ed
bake bakery bak+ery
dedicate dedication dedicat+ion
establish establishment establish+ment
The words in the centre column can be broken down into parts, as indicated in the right-hand column. It is not obvious that those in the left-hand column can be factored in the same way.
A monomorphemic word like 'help' is structurally complex in one sense; it can be decomposed into distinct phonological elements (sounds, if you will), each associated with some configuration of the speech organs. The same is true of 'helped' of course, but that is not what leads up to segment 'helped' into two morphemes: help+ed (/help+t/). The intuition that leads us to divide 'helped' into two parts is that each part is associated with a meaning. Thus, the usual definition of morpheme is something like the following:
A morpheme is the minimal unit of linguistic expression that is associated with a meaning.
The term 'duality of patterning' was current in the 1960's to refer to this design feature of human language; that phonological objects without meaning combine to form meaningful atoms, which themselves combine to form complex linguistic expressions.
Types of Morphemes
The standard typology of morphemes classifies them according to their:
freedom of occurrence
mode of attachment
Free and Bound Morphemes
Free morphemes are those that can occur alone, as monomorphemic words; bound morphemes always occur in combination with some other morpheme:
It is often the case, in a morphologically-complex word, that none of the component morphemes are free, as in: ante+diluv+ian
or in the set:
*gress aggress aggression aggressive
digress digression digressive
regress regression regressive
or, conversely, that none are bound:
Root, Stem, and Affix
In the following table, the words in each row and in each column have a morpheme in common (with some allowance for column 1):
work seem live book
works seems lives books
working seeming living booking
worked seemed lived booked
But we would also probably want to say that the forms in the same column are more closely related to one another than those in the same row. We might think of the former as "different forms of the same word", while the latter accidentally happen to share a morpheme.
In a morphologically complex word, the morpheme that carries the central element of meaning is the root morpheme; those bound morphemes that operate on or modify the meaning of the root are affixes. So, in the above table, the rows share a common root, and the columns, a common affix. Morphologically-complex forms like those in the final set in the preceding section have more than one root...