I am searching for a nice book to seriously learn the homology theory in algebraic topology with. I am looking for a book that starts with (or gets quick to ) the axioms of homology theory. I looked into several books before, which are either to advanced (Homotopical Theory by Fomenko and Fuchs, which I would love to study, but it is kind off weird), or do not exactly contain what I am searching for right now (An Introduction to Algebraic Topology by Rotman). Also some german textbooks on the topic, one of them seems fitting but assumes to much prior knowledge and advances therefore to quick (module theory, homological algebra, the needed category theory, difficult to read notation wise).
So is there a (pretty much) self contained textbook you would recommand on the topic?
Not everything needed for the book has to be covered of course, but I feel like many books on algebraic topology are hard to get into, and I am looking something to seriously get started in this field, and gets quick to applications and calculations of the developed theory. So if you name a book and some other sources to get used to backround stuff, that would fit too.
Looking forward to your recommandations! Thanks in advance.
Edit: When commenting, please do not just name a title, but also why you seem that this book fits, or what you liked about the book. This would help me.