What are good resources to learn about convergence spaces? 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.
 A: There is a new (2016) textbook which covers convergence spaces and related concepts:


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*"Continuity Theory" by Louis Nel
A: Some suggestions:


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*Basic Properties of Filter Convergence spaces

*On the theory of convergence spaces
and references therein. I'm also quite interested to learn about new resources, especially ones with lots of (worked) examples to get a feel for the difference between, say, a pseudotopological and a pretopological convergence, etc.
The motivation for their study often seems category-theoretical (convergence spaces are Cartesian closed, e.g.). I would also like to see a good list of open problems, e.g.
This page offers a general overview of "topology-like" classes of spaces, and I once read parts of the book: "G. Preuss, "Topological structures—An approach to categorical topology" , Reidel (1988)", which mostly talks about category constructions (like initial and final structures), it seems appropriate in view of your tags.
A: Additionally, there is:


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*"Problems in the Theory of Convergence Spaces" by D. R. Patten

*"Grundstrukturen der Analysis" I & II by W. Gähler, if you understand German


Also "Handbook of Analysis and its Foundations" by E. Schechter deals briefly with convergence spaces (and pretopological spaces).
A: The one I'm reading is Convergence Structures and Applications to Functional Analysis by R. Beattie and Heinz-Peter Butzmann.
I've liked it so far, and starts with Convergence Spaces right away. Worth taking a look, specially for the ones that like Analysis.
