TITLE: Best Algebraic Topology book/Alternative to Allen Hatcher free book?
QUESTION [57 upvotes]: Allen Hatcher seems impossible and this is set as the course text?
So was wondering is there a better book than this? It's pretty cheap book compared to other books on amazon and is free online. 
Any good intro to Algebraic topology books?
I can find a big lists of Algebraic geometry books on here. On a very old thread on Maths overflow someone recommended that a person should read James Munkres Topology first, then you should read Allen Hatcher book. 
It just seems like Rudin's book but crammed with ten times more material.

REPLY [7 votes]: There is a really well-written but lesser known book by William Fulton. That's the book I learnt Algebraic Topology from. The chapters are laid out in an order that justifies the need for algebraic machinery in topology. A guiding principle of the text is that algebraic machinery must be introduced only as needed, and the topology is more important than the algebraic methods. This is exactly how the student mind works.
The book does a great job, going from the known to the unknown: in the first chapter, winding number is introduced using path integrals. Then winding number is explored in a lot more detail, and its connection to homotopy is discussed, without even mentioning fundamental groups. Then a number of results like the Fundamental Theorem of Algebra, Borsuk Ulam and Brouwer's Fixed Point Theorem are proved using winding numbers.
Only in Ch.5 do we see the first algebraic object. Here again, the order is flipped: the first De Rham Cohomology group is introduced and used to prove the Jordan Curve Theorem. Then homology groups of open sets in the plane are discussed, and the connection between homology and winding number is made clear. A number of applications to complex integration etc are discussed, and the Mayer-Vietoris theorem is proved for n=1.
Covering spaces and fundamental groups are introduced after homology, another novelty. Higher dimensions are encountered only towards the end of the book, but by the time we get there, we already know the general idea behind all the concepts.
Very few books take this point of view of developing intuition clarity before generalising rapidly. I think this is really helpful because before studying the general theory of anything, we need to know what it is we are trying to generalise.