What are good resources (books, lecture notes, introductory papers, ...) to learn about convergence spaces?
I read in an answer to a recent question the following:
There's still a subtle issue. If you try to axiomatize topological spaces via filter convergence, you wind up with a significantly more general notion called a convergence space. Convergence spaces are really nice, and personally I wish people would start treating them as the basic objects of interest in general topology, and treat topological spaces as a mere special case. Unfortunately, I haven't been able to find an elementary introduction to such things that I can link you to, so you'll have to learn things the classical way until you're ready to go off on your own.
This sounds quite intriguing, so I thought it might be reasonable to ask where to look if I decide to learn a bit more about convergence spaces.