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!



A comprehensive overview of finite fields
[Finite Fields](http://books.google.com/books?id=xqMqxQTFUkMC) by R. Lidl and H Niederreiter (CUP). Probably as comprehensive as it gets.  

The ams review calls it the ``the Bible of finite fields''. You can find it (the review)[here](http://www.ams.org/bull/1999-36-01/S0273-0979-99-00768-5/S0273-0979-99-00768-5.pdf).


