Constructing Topological Spaces — A Primer by Jeremy Kun.
From the post:
Last time we investigated the (very unintuitive) concept of a topological space as a set of “points” endowed with a description of which subsets are open. Now in order to actually arrive at a discussion of interesting and useful topological spaces, we need to be able to take simple topological spaces and build them up into more complex ones. This will take the form of subspaces and quotients, and through these we will make rigorous the notion of “gluing” and “building” spaces.
More heavy sledding but pay special attention to the discussion of sets and equivalences.
Jeremy concludes with pointers to books for additional reading.
Any personal favorites you would like to add to the list?