Can anyone summarize what conformal field theory is actually about,i.e.
1) what are its goals? (for example, to study such-and-such fields/functions/maps/etc. to see whether they have such-and such properties, and what it means)
2)it is described as "a quantum field theory". How many quantum field theories are there then? Which one does this correspond to. I don't have background in QFT but I thought the division was only between bosonic/fermionic fields.
3) which techniques it uses? (for example, perturbation expansion)
I know there are many good books and references, but I was wondering if I could get a self-contained answer here. A few questions have been asked on this website, but none address my two questions above in a straightforward way, without referencing to books. I have a background in quantum mechanics and classical electrodynamics.
Any help will be appreciated! Even if it just involves broad analogies!