Morphology
The morpheme

Source of the picture: gumtree.com
'They gave it me', Humpty Dumpty continued thoughtfully, as he crossed one knee over the other and clasped his hands round it, 'they gave it me--for an un-birthday present.'
'I beg your pardon?' Alice said with a puzzled air.
'I'm not offended,' said Humpty Dumpty.
'I mean, what IS an un-birthday present?'
'A present given when it isn't your birthday, of course.'
Carroll, Lewis: Through the Looking Glass
Understanding words is an intrinsic part of our knowledge of language. Although we hardly ever consciously think about words, that is, the way they are either structured or formed, we still know how to use words in both written and spoken communication.
In the brief, yet hilarious dialogue both Alice and Humpty Dumpty know that the morpheme "un-" refers to "not". So do we as the readers.
Morphology strives to analyze the underlying internal structure of words: its most basic unit of analysis is the so-called morpheme, e.g. "un-" as in "un-birthday" or "de-" as in "to decompose". A morpheme is – by definition – the smallest meaningful unit into which each word can be decomposed.
A word may consist of one or more morphemes, which shall, however, not be confused with its prosodic elements, i.e. its syllables. Along these lines, the verb moralize contains the three syllables mo-, ra-, lize, but only two morphemes – namely moral and –ize. Compare the syllables and the morphemes and you will realize that, contrary to the syllables, each morpheme in “moralize” has a stable “meaning”, which remains the same even if the respective morphemes appear in a different context, e.g. in im-moral or in morality.
Most apparently, independently of the word in which they occur, the morpheme moral has the lexical meaning of “ethic”, while the morpheme –ize attached to the base signifies the word’s grammatical category as a verb. Morphemes, therefore, always present a form-meaning-pairing in the Saussurean sense.
Words consisting of more than one morpheme are termed polymorphemic or complex words; in contrast, words that contain only one morpheme, such as the word albatross, are called monomorphemic or simplex words.