This paper is a cook's tour of homotopical algebra, from it's origins
in Combinatorial Topology in the early part of the century, through
the work of Eilenberg-Mac Lane, Kan and Quillen, to modern
applications related to sheaves and presheaves of simplicial sets in
areas related to algebraic K-theory. The paper is intended as an
introduction for algebraists to combinatorial homotopy theoretic
concepts.
An updated version has been submitted, so this one has
been removed.