Rigorous text book on algebraic topology I learned basic algebraic topology before, contents including homotopy lifting lemma and covering space and Van Kampen theorem and etc. (The class used Hatcher's Algebraic Topology when I took this course) 
However, I have never learned things related to homological algebra. I'm taking algebraic topology dealing with homological algebra this semester, so I wonder if there is a rigorous text on this side of algebraic topology.
Personally, I do not like Hatcher's style of text. It is not that much formal in my sense and materials are not well-ordered. (For example, he proves a very special case then after few pages, he states a theorem which is more general, then just notes there that copy the idea of the proof before he handed) I personally like rigor, formal, and axiomatic approaches even if text may seem dry. For example, I like Rudin's and Folland's and Mukres' and Dummit's and Rotman's styles of texts and etc, but I dislike Stein's and Hatcher's styles of texts.
Moreover, I have seen a post saying that "Hatcher uses $\Delta$ complexes, which are rarely used". So what would be the standard complexes? And what text develops theory using that complexes?
Thank you in advance! :)
 A: tom Dieck's Algebraic Topology is great. It is very rigorous, presents an incredibly wide range of topics, uses (admittedly minimal) categorical language, and gives a much more homotopical perspective on many things.
A small but large detail I always remember is that Hatcher's proof of homotopy invariance of singular homology is not very useful for generalization, but tom Dieck's, which inductively constructs a natural homotopy, leads to the acyclic models theorem, from which several other (otherwise tough) theorems follow.
A: Our tastes are pretty much the same. So, from my experience, I would recommend Spanier's algebraic topology.
It's highly rigorous (just like an analysis or algebra book), and many results are formulated in categorical languages. Besides, assumptions are often as weak as possible. 
There are also some downsides. First, there aren't many examples, though there are some examples to illustrate some assumption is necessary. Second, I don't know why the author didn't use much of CW complexes. Instead, simplicial complexes are used extensively. 
Overall, it's a very classic book. Hope you'll like it.
