As always it depends on what you know (i.e. your background) and on what you need. For Galois theory, there is a nice book by Douady and Douady, which looks at it comparing Galois theory with covering space theory etc. Another which has stood the test of time is Ian Stewart's book.

For Lie groups and Lie algebras, it can help to see their applications early on, so some of the text books for physicists can be fun to read. They skip some detail but provide the intuition that is sometimes lacking in purely mathematical texts.