TITLE: Reference textbook developing NBG set theory
QUESTION [7 upvotes]: I'm starting Borceux "Handbook of Categorical Algebra". It starts with a brief discussion of the logical foundations of category theory.
He describes two approaches: 1.defining universes and 2. With NBG set theory.
I'm interested in the second approach, so I want to study the axiomatics of that system. 
The book that I'm looking for should present the logical construction of the theory and some important results such as proving that NBG is an extension of ZFC, some results on model theory and a profound discussion of its applicability to category theory if possible.

REPLY [2 votes]: Two references which list the axioms of NBG are
(1) Chapter one of Godel's 1940 monograph titled "The consistency of the axiom of choice and the generalized continuum hypothesis from the axioms of set theory"
(2) Chapter II article 7 in Foundations of set theory by Fraenkel, Bar-Hillel and Levy.
Remark: NBG is a conservative extension of ZF - See pages 131-32 in reference (2) above for a proof sketch. Although NBG is finitely axiomatizable, this is not a real advantage. Godel used this system in (1) only to have a more economical definition of the constructible universe.
There is also a system called Morse-Kelley (stronger than ZF) about which you can read in the appendix of Kelley's General topology and also on Wikipedia.