Connections with cohomology
Hatcher §4.3 (pages 393–420). Mapped, not yet decomposed.
Cohomology turns out to be homotopy theory in disguise: Hⁿ(X; G) is
naturally the set of homotopy classes of maps from X into an
Eilenberg–MacLane space K(G, n). The section proves this, develops fibrations
as the tool that makes such arguments work, builds Postnikov towers to
decompose a space by its homotopy groups, and uses them for obstruction theory,
which measures when a map defined on a skeleton extends.
Nothing here is upstream, and it depends on Chapter 3's cohomology as well as on elementary methods of calculation.