This paper undertakes to exploit the observation that the non-abelian homological algebra of Quillen and, in particular, the commutative algebra homology of André and Quillen provides a framework for discussing the unstable Adams spectral sequence of Bousfield and Kan. We take this observation in a variety of directions ; for instance, we show that the long exact “transitivity sequence” in the sequence of a fibration, and we show that a product in André-Quillen cohomology is related to the homotopy long exact sequence of a fibration, and we show that a product in André-Quillen cohomology can be used to compute the Whitehead product in homotopy.