Point set topology Some time back, I tried reading Rudin's Principles of Mathematical Analysis and I found no trouble with the introductory chapter. In chapter II I encountered point set topology. The number of theorems packed into some pages kind of overwhelmed me. I got stuck there as I felt I did not fully understand everything geometrically. I thought topology was supposed to be geometric.
So, I request you to suggest something in this regard. I am contemplating learning some basic point set topology from elsewhere (I don't know where from) and I am wondering if this is the solution to my problem. (Yes, as a preparation for analysis. Even some good notes would be nice or perhaps a great book)
Any help is appreciated.
PS: I hate compromising rigor. 

If you are looking for a gentle introduction to basic topology ideas with examples and explanations which give some intuition about what is going on, I would recommend that you could have a look at Simmons book "Introduction to Topology and Modern Analysis".
It is available from Amazon here. Some of the reviews on that page are pretty good, and I would not disagree.
