Any theory of syntax in which linguistic output (SurfaceStructure?) is related to a deeper level of mental representation (DeepStructure) by a set of transformation rules that move constituents in DeepStructure into the order they appear in SurfaceStructure?. Note that different theories of TransformationalGrammar have different names and functions for these levels, and some have more levels. The key is the derivation of surface forms (i.e., the sentence you actually say) from some deeper level of representation.
TransformationalGrammar was developed by NoamChomsky. Other, non-transformational theories of syntax include HeadDrivenPhraseStructureGrammar, LexicalFunctionalGrammar?, and CategorialGrammar?.
Add GenerativeSemantics? - Lakoff, Ross and McCawley, dissidents who broke off from Chomsky. (Disclaimer - the late Jim McCawley was my dissertation adviser and good friend.) -- TomRossen