This article is from the sci.lang FAQ, by Michael Covington (mcovingt@ai.uga.edu) and Mark Rosenfelder (markrose@zompist.com) with numerous contributions by others.
The scientific study of human language, including:
Phonetics (physical nature of speech)
Phonology (use of sounds in language)
Morphology (word formation)
Syntax (sentence structure)
Semantics (meaning of words & how they combine into sentences)
Pragmatics (effect of situation on language use)
Or, carving it up another way:
Theoretical linguistics (pure and simple: how languages work)
Historical linguistics (how languages got to be the way they are)
Sociolinguistics (language and the structure of society)
Psycholinguistics (how language is implemented in the brain)
Applied linguistics (teaching, translation, etc.)
Computational linguistics (computer processing of human language)
Some linguists also study sign languages, non-verbal communication,
animal communication, and other topics besides spoken language.
 
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