Is Suppes' Axiomatic Set Theory standard?

I've read 'Axiomatic Set Theory' by Patrick Suppes, and one thing I've noticed throughout is that he seems to be obsessed with definitions, and he tries to allow for urelements. Is this standard for ZFC?

I thought in general when we say 'set' in ZFC we really mean 'pure set', and so avoid having to worry about individuals. In addition I've never seen such a fuss over definitions in any other mathematical book I've read, is this something I should get used to in Set Theory?

If this is not standard, can anyone direct me to a book similar to Suppes' which builds (from the axioms) all the usual set theoretical structures needed for other areas of mathematics that is?

• Only a comment - if you forbid ur-elements, you are nor more allowed to use examples like : the set $\{ John, Jim \}$ ... unless you show how to "build up" e,g, $John$ starting from $\emptyset$. – Mauro ALLEGRANZA Sep 12 '15 at 15:48