Source : WordNet®

set theory
     n : the branch of pure mathematics that deals with the nature
         and relations of sets

Source : Free On-Line Dictionary of Computing

set theory
     
         A mathematical formalisation of the theory of
        "sets" (aggregates or collections) of objects ("elements" or
        "members").  Many mathematicians use set theory as the basis
        for all other mathematics.
     
        Mathematicians began to realise toward the end of the 19th
        century that just doing "the obvious thing" with sets led to
        embarrassing {paradox}es, the most famous being {Russell's
        Paradox}.  As a result, they acknowledged the need for a
        suitable {axiomatisation} for talking about sets.  Numerous
        such axiomatisations exist; the most popular among ordinary
        mathematicians is {Zermelo Frankel set theory}.
     
        {The beginnings of set theory
        (http://www-groups.dcs.st-and.ac.uk/~history/HistoryTopics.html)}.
     
        (1995-05-10)