As discussed in the course outline, the textbook for the course will be
Munkres' book is quite standard for a challenging undergraduate-level course in this topic. There are also many other undergraduate-level topology books, however, a few of which I'll name.
The following textbook has many nice examples, which I like a lot. It is out-of-print, but you may be able to find a copy on the internet.
A free textbook is by Morris. The last word of the title may be read either in the sense of weeping or ripping.
Another recent textbook is by Waldmann, and looks fairly readable.
The next book I'll mention takes a somewhat different approach, introducing topology through combinatorial examples such as polyhedra and generalizations. If you're interested in these directions, you might like to look through this textbook.
A couple of other textbooks that come well-recommended, but which I haven't examined closely, are:
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 should be fairly readable.