Patrick Morandi's Field and Galois Theory is a good book for beginners. He gives lots of examples and has interesting exercises too. For a later reading though, I would suggest the Galois theory section in Lang's Algebra.

I really liked Hsiang's Lectures in Lie Groups although it may be a bit short for a full course. And Kirillov Jr.'s book Introduction to Lie Groups and Lie Algebras (also available as a published book) is a very good introduction to the topic with plenty of nice examples in the exercises. And lastly, Serre's Complex Semisimple Lie Algebras is great once you manage to get through it, i.e., it's a gem but not for the first reading!