A lot of "big" names in analysis (and other fields) seem to be doing some form of combinatorics (without any order, some examples are Tim Gowers, Terence Tao and Jean Bourgain).
So, looking a bit around makes me conclude that combinatorics is a huge field. There must be one "kind" which is the most fruitful in analysis. What kind is this? What is a good introduction to this?
Edit: I forgot, analysis is also a big field. I mean more in the direction of harmonic analysis and PDE.