TITLE: A book about model theory
QUESTION [7 upvotes]: 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...

REPLY [2 votes]: I might be completely mistaken, but I dare say you should take a look at set theory first, maye that could clarify your questions.
I'd recommend the first four chapters of Kenneth Kunen's book, at least they helped my understanding, but maybe that's not the thing you had in mind.
In particular:
Chapter 1, §14: "Formalizing the metatheory"
Chapter 4, §9: "Model theory in the metatheory"
Chapter 4, §10: "Model theory in the formal theory"