  Braces and linear cycle sets are algebraic structures playing a major role in
the classification of involutive set-theoretic solutions to the Yang-Baxter
equation. This paper introduces two versions of their (co)homology theories.
These theories mix the Harrison (co)homology for the abelian group structure
and the (co)homology theory for general cycle sets, developed earlier by the
authors. Different classes of brace extensions are completely classified in
terms of second cohomology groups.
