Exercises on Galois Theory

I really like the exercises in Lang's Algebra. There's a little bit of everything in there.

Milne's notes have exercises at the end of every chapter, a chapter of review exercises, and a two-hour exam; solutions (or at least hints) for all of these are given at the end. A lot of the action takes place over $\mathbf Q$, but I saw a fair number of questions about finite fields and they seemed good.

Keith Conrad's handouts don't have a lot of exercises, but when I had to review this stuff I found it helpful to look at the statements of his examples, try them for myself, and then read his methods. There are usually myriad ways to solve exercises in this area.

Teruyoshi Yoshida has fun example sheets, in addition to complete course notes.

Try these books:

• Classical Galois Theory with Examples
• Exploratory Galois Theory
• Galois Theory for Beginners: A Historical Perspective

Many pages of exercises at J K Verma's website, here.