# A comprehensive overview of finite fields

I've read numerous introductions to finite fields, but I feel like my intuition about them is fairly lacking. Considering that finite fields are the the most "inert" objects in algebraic geometry, I think I could use a serious surge of perspective.

What I would like to read now is a comprehensive overview that tells me "everything I need to know" about how finite fields and their algebraic closures work, algebraically. I don't mind working out the proofs on my own if they are terse or absent; I'm just looking for quality and quantity of results. Hopefully some intense reading will help steep out some of my insecurities about characteristic p.

Can anyone recommend a single source for such an overview?

Thanks!

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If you are a geometer over finite fields, then the Frobenius will make sure that you are almost as good as in the algebraically closed case. Befriend the Frobenius, and then you are in a safe position. –  Regenbogen Feb 26 '10 at 0:15

The ams review calls it the the Bible of finite fields''. You can find it (the review)here.
The really important things in algebraic number theory start from group cohomology and theorems like Hilbert 90, but you'll be better searching/asking for different keywords than finite fields then.