I am looking for the most basic but rigorous to some extent book on Algebraic topology out there.
I've got Greenberg and Harper beside me. It looks formidable/impossible due to as you say not many words.Greenberg and Harper has the virtue of not using too many words
I think Hatcher's beautiful book is an important addition to the roster, but probably that it is intended for students who aren't feeling overwhelmed.
It's not!Algebraic topology for dummies?
Should be Wallace; "Differential Topology, First Steps"?i also recommend massey's book on differential topology, first steps.