As discussed in the course outline, the textbooks used in the course will be
These two books take a somewhat different approach. Hatcher's book tends to be better at giving some intuition. Munkres' book tends to be a little more careful and understandable with some of the definitions and foundational material. I'll try to indicate which one I think is better to read from each week.
Another book that you might like is by Alexandroff. Although this book is somewhat older (and may be a little harder to read in some places for that reason), it tries to take an intuitive and engaging approach, and at the very least it is fairly short.
In addition to the book on algebraic topology, Munkres also has an undergraduate book. This has a fair bit on the fundamental group (a somewhat different approach to algebraic topology than the homology we will discuss here), and a small amount on homology (only as far as H1). This won't get you very far, but if you like this book, then you might like looking through these sections.
A lower-level book that does have a reasonably sophisticated treatment of homology (as well as of ideas such as simplicial complexes is the following.
We can have a lively online discussion in the UP e-classroom system. Asking and answering questions of your peers will be of great benefit to your development.
Wikipedia has a number of articles on mathematical topics. They are mostly well-written and accurate, and many of the articles relevant to the content of Topology and homology theory should be fairly readable.