  This expository article sets forth a self-contained and purely algebraic
proof of a deep result of Quillen stating that the category of simplicial
commutative algebras over a commutative ring is a model category. This is
accomplished by starting from the model structure on the category of connective
chain complexes, transferring it to the category of simplicial modules via
Dold-Kan Correspondence, and further transferring it to the category of
simplicial commutative algebras through Quillen-Kan Transfer Machine. The
subtlety of overcoming the acyclicity condition is addressed by introducing and
studying the shuffle product of connective chain complexes, establishing a
variant of Eilenberg-Zilber Theorem, and carefully scrutinizing the subtle
structures under study.
