MATHEMATICAL LINGUISTICS is the study of mathematical struc- tures and methods that are of importance to linguistics. As in other branches of applied mathematics, the influence of the empirical subject matter is some- what indirect: theorems are often proved more for their inherent mathemat- ical value than for their applicability. Nevertheless, the internal organization of linguistics remains the best guide for understanding the internal subdivi- sions of mathematical linguistics, and we will survey the field following the traditional division of linguistics into → Phonetics, → Phonology, → Mor- phology, → Syntax, and → Semantics, looking at other branches of linguistics such as → Sociolinguistics or → Language Acquisition only to the extent that these have developed their own mathematical methods.