Hi,
I wish that folks would not determine "jazz" as a style, since there is such an incredible individuality within it to even discuss it.
You can listen to Garbarek, Davis, Jarrett, Rypdal, McLoughlin and specially European folks, that do not follow the rudimentary American style of jazz, and often less melody based. But that might be a simple preference of mine, so please excuse me on that.
I have always thought that if anything, the jazz thing is more about the individuality than anything we can define. I guess that learning some "basics" is a nice start, although I tend to think that is just another door that you have to open later, in order to get out and free yourself?