This is related to one of my other open questions. But more generally than my question there, I've found it difficult to teach myself "low dimensional" (i.e. 2 or 3-dimensional) category theory. The n-cat lab is helpful in this regard, but often there is not enough detail presented in the articles to really allow the reader to grasp the concept (beyond just the basic definitions).
Specifically what I'm looking for is a book (or perhaps some lecture notes, or some papers) that detail how one might generalize the usual theorems about the 2-category Cat (i.e. adjoint functor theorem, Yoneda lemma, etc...) to arbitrary 2-categories. In other words, I am looking for a detailed exposition of what is known about the 3-category of 2-categories.
John Gray's book "Adjointness for 2-Categories" is probably the closest thing to this that I can think of, but according to the n-cat lab, the content of the book is rather out-dated.
So are there any similar references to "Adjointness for 2-Categories" which are more up to date, or am I best served just by reading it and translating Gray's terminology into the more modern terminology in my head?
Also, I suppose I should mention: Given a lack of materials specifically for low-dimensional cateogry theory, I would also be satisfied with a reference for the more general $n$-categorical notions, provided that a similar theory (i.e. for the $n+1$ category of $n$-categories), detailing the generalized Yoneda lemma, adjoint functor theorem, etc... is developed.