I have been studying galois theory on my own and find it very fascinating. I have gone through Ian Stewarts book: http://www.amazon.co.uk/Galois-Theory-Third-Chapman-Mathematics/dp/1584883936. I am not sure which book to study from next but I would like to learn about something along the lines of algebraic closures of Q and other related topics.
Related to this, I would also like to learn more finite field theory. I would like books that are not too technical and provide some context since I am doing a self study.
Best Answer
For more advanced material, you might like to try Askold Khovanskii: Galois Theory, Coverings, and Riemann Surfaces.