I know that we can do a lot of 2-category theory, seeing 2-categories as Cat-enriched categories. Yet, I know that there are some limitations of this approach.
I also know that there are many articles which could help to understand 2-category theory... (I am only familiar with a few of the Lack's, Street's and Kelly's articles so far, but I know there are many more important articles).
But always when I'm trying to deal seriously with 2-categories, I end finding serious difficulties.
So I am sure I have to improve my 2-category theory knowledge in general. And just recently I have become aware of the Gray's Formal Category Theory. So my question is about basics of 2-category theory: which set of articles or books could be considered as a solid base to start thinking seriously about 2-category theory?


I am just trying to avoid a common situation for me: being stuck in a well known (and basic) subject of 2-category theory, ignoring the existence of (classical) literature about this subject.


Thank you in advance 



2-category theory
One aspect of 2-category theory which I've sometimes found difficult or tricky is 2-limits (or variants thereof). If that is troubling you too, some of these papers (mentioned in the nLab article on 2-limits) could be helpful: 


* Ross Street, *Limits indexed by category-valued 2-functors*, Journal of Pure and Applied Algebra, Volume 8 No. 2 (June 1976), 149–181. [link](http://www.sciencedirect.com/science/article/pii/002240497690013X)
* Max Kelly, *Elementary observations on 2-categorical limits*, Bulletin of the Australian Mathematical Society (1989), 39: 301-317, [link](http://journals.cambridge.org/abstract_S0004972700002781).
* Ross Street, *Fibrations in Bicategories*, Cahiers de topologie et géométrie différentielle catégoriques, tome 21, no. 2 (1980), p. 111-160. [numdam pdf](http://archive.numdam.org/ARCHIVE/CTGDC/CTGDC_1980__21_2/CTGDC_1980__21_2_111_0/CTGDC_1980__21_2_111_0.pdf). See also the Correction (same journal, Vol. 28 No. 1 (1987), 53-56). [link](https://eudml.org/doc/91390)
* Steve Lack, *A 2-categories companion* [arXiv:math.CT/0702535](http://arxiv.org/abs/math.CT/0702535) (see section 6, page 37).
* G.J. Bird, G.M. Kelly, A.J. Power, R.H. Street, *Flexible limits for 2-categories*, Journal of Pure and Applied Algebra, Vol. 61 No. 1, (November 1989), 1–27. [link](http://dx.doi.org/10.1016/0022-4049(89)90065-0)
* Thomas Fiore, *Pseudo Limits, Biadjoints, and Pseudo Algebras*, [arXiv:math/0408298](http://arxiv.org/abs/math/0408298); see chapters 3, 4, 5.
* John Power, *2-categories*, BRICS Notes Series NS-98-7, ISSN 0909-3206 (August 1998). [pdf](http://www.brics.dk/NS/98/7/BRICS-NS-98-7.pdf)


