Literature on finite fields??

Question

Finite fields occupy an important and elementary part of number theory, but I can’t seem to find good literature on this topic. Can anyone help me?

Answer 1

I found Introduction to finite fields and their applications by R. Lidl and H. Niederreiter very helpful.

Update: This book (or better a successor version) is also available as volume 20 in the Cambridge series Encyclopedia of Mathematics and its Applications indicating its high quality status.

It is titled Finite Fields. The first six chapters are essentially the same. Chapter V has been extended by three sections: Jabobi Sums, Character Sums with Polynomial Arguments and Further Results on Character Sums. The final four sections have been extended and somewhat rearranged.

Answer 2

Fried, Michael D.; Jarden, Moshe, Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge 11. Berlin: Springer (ISBN 3-540-22811-X/hbk). xxii, 780 p. (2005). ZBL1055.12003.

Is the book many experts use.