I'm an undergrad with minimal experience in proof-based classes, and I'm in a pickle with a current course.
Normally, I have trouble understanding and/or retaining information during lectures, so I take notes and then read the textbook at home and practice doing problems/writing proofs. So far it has worked just fine. I think I've learned everything thoroughly and I tend to be at the top of my classes in terms of test grades.
I am now in a beginning topology course (only relevant previous course I've had is a beginning real analysis course) and it is taught very differently. There is no textbook, and the only notes are ultimate results (theorems, exercises, corollaries, etc.) and a few definitions. All of the direction on proofs are discussed in class, mainly between other students and the instructor. I get why this is a reasonable way to teach the material, but since I have trouble with understanding the concepts during real-time discussions, I feel VERY behind. I don't know if any of my proofs are adequate, and I can only ask so many questions in class or at office hours. I really miss having a discussion of concepts/proofs that establish concepts that I can read over a thousand times if I want to. One small thing gets covered in class and I spend some time working through it in my head, proving it to myself, and then when I am satisfied I understand it I zone back in and I've missed 10 more things.
So first, are there any textbooks that could help here? I've looked at Munkres, but I figured others here might have better suggestions. I'm also open to advice, if anyone's been in a similar situation before, or at least have good approaches to tackling topology in particular.