TITLE: Textbooks for axiomatic approach to algebraic topology
QUESTION [5 upvotes]: Are there textbooks on algebraic topology which first starts with the Eilenberg-Steenrod axioms and then derives consequences and applications directly out of the axioms. Only at the end they show there are indeed theories which satisfy the Eilenberg-Steenrod axioms.

REPLY [2 votes]: How about Foundations of Algebraic Topology, by none other than Eilenberg and Steenrod.