Complex Analysis is a very broad branch of mathematics. I am currently self-studying the foundations of it, and I would like to know what are the major 'paths' which stems from (or are contained in) Complex Analysis, sometimes called Complex Function Theory, and what are the major paths within the subject? For example, I know there is the 'value-distribution' 'part' of it, for example Nevanlinna Theory, but I do not know many other areas.
Thank you in advance.
For questions like this, perhaps a good source is the Mathematics Subject Classification now used by both MathSciNet and zbMath.
Here are the main headings related to complex analysis.
That site is interactive. You can get the subheadings of each of these "xx" headings. For example here is 30C: