2d CFT versus higher dimensions I am starting a reading course this quarter in conformal field theory. Is it necessary to do CFT in 2 dimensions first in order to understand it in 3 or greater dimensions, or would I be able to just start off in 3 or greater? Or is there a good reference that treats them simultaneously?
 A: In my opinion, any course in specifically 2d CFT will not be particularly useful if your aim is 3d and higher. At least I am not aware of any counterexamples.   
The reason is that in 2d the central topic is Virasoro symmetry, which is not available in higher dimensions. You could think that a 2d text would address stuff useful to higher dimensions before going to Virasoro symmetry, but that doesn't happen, since the questions which are highly non-trivial in higher dimensions are completely trivial in 2d (e.g. operators with spin, correlators of operators with spin, $SO(d+1,1)$ conformal blocks, etc.)
So, answering the first part of your question, if you understand higher dimensional CFT's, you will certainly understand the non-Virasoro aspects of 2d CFT's, but going the other way around is probably not going to help. If your goal is higher dimensional CFT's, you might not want to waste your time on exclusively 2d texts (which is not to say that the full 2d story is not worth learning).
For higher-dimensional CFT references, I would suggest David Simmons-Duffin's TASI lectures on conformal bootstrap and Slava Rychkov's EPFL lectures and references therein. These are perhaps mostly oriented towards conformal bootstrap applications. Joshua D. Qualls' lectures treat both 2d and higher-d, so may be a good start if you are not familiar with the 2d story.
It is also worth stressing that the higher-dimensional CFT's are a topic of active research, and a lot of important material exists only in papers (for example, most of the story for operators with spin). The references in the above lecture notes can hopefully serve as a good guide.
