Mentioned in Weibel as important. Can be regarded as a special case of Quillen homology, see Goerss and Schemmerhorn.
Commutative rings??? See Weibel’s book. Can also generalize to schemes, see Illusie: LNM239.
Iyengar (I think many different articles).
Weibel: An introduction to homological algebra.
arXiv: Experimental full text search
NCG (Algebra and noncommutative geometry), AG (Algebraic geometry)?
Swierczkowski in LNM0137 shows that Andre homology is a special case of Barr-Beck homology. Both notions are explained. Ref to Andre LNM0032 Methode simplicial… and Barr and Beck LNM0080 Homology and standard constructions, the latter I think describing triple cohomology.
nLab page on Andre-Quillen homology