What textbooks on higher category theory are there? What books do you recommend? I am looking for self-contained introductions, no research reports. There are lots of informal summaries and arXiv papers, but I am really only asking for textbooks here.
I know of Lurie's Higher Topos Theory, which "only" treats $(\infty,1)$-categories. I am looking for books which treat $\infty$-categories in general. Then I know of Leinster's Higher Operads, Higher Categories, which is from 2004. Is it still up to date? Is Leinster's book the best introduction to the subject? What do you think of Higher-Dimensional Categories: an illustrated guide book by Cheng and Lauda, which is also from 2004 and still a draft? Is it too informal when one really wants to work with the concepts?
Bonus question: Meanwhile, is there some "preferred" definition of an $\infty$-category among the dozen definitions which have been studied?