I am looking for a good book about model theory. As this is obviously too vague, let me explain what I am looking for and why.

First I am interested about the basics and foundations of model theory. Right now I am not interested in their applications (like proving things in mathematics or even independence results like Cohen's -- but of course it is not a problem if a book deals with some of these applications if it does not *only* that).

Second, until a few days ago I believed I knew well enough what was a model.
But since two days I am not so sure. **I have a problem with the notion of model inside ZF (or ZFC, or any formalized set theory) of a theory, and in particular, with the meaning of the satisfaction relation in this case.** I would like a book which treats that aspect.

These problems arose with my trying to understand the answers to my question A meta-mathematical question related to Hilbert tenth problem

I am currently having endless discussions in comments about that notion what I am said doesn't make sense to me (and the converse is clearly also true). A good book will certainly help me and save time for my respectable interlocutors. Thanks...