I have a lot of time on my hands and want to work on learning some higher level topic in analysis, but one that helps me stay in touch with (and get better) at "standard" topics in analysis. What are some topics in analysis that aren't covered by 'intro to analysis' classes but capture a lot of different ideas in analysis? An example would be functional analysis, which is incomplete without understanding thoroughly functions, sequences, compactness, linear algebra techniques, etc.
What some are other, more specific, higher-level topics in analysis that reinforce understanding of basic techniques? I guess all topics do this to some extent, but I'm looking for topics that do this to a significantly great extent.
My experience until now: I'm comfortable with basic analysis (intro to analysis classes), some topology, some functional analysis, some stuff with smooth manifolds.
