The Galois connection between syntax and semantics
Peter Smith, The Galois connection between syntax and semantics.
explains Lawvere’s remark about ‘the familiar Galois connection between sets of axioms and classes of models, for a fixed [signature]‘
Seems like a rather nice introduction to the notion of Galois connection (I seem to remember someone asking about this awhile back).
One place Galois connections pop up is in the realm of Abstract Interpretation.