The course ran October to December 2013. This should be the final version of this web page now. Drop me (mylastname at imperial.ac.uk) a line if something here is broken or missing.
Sheet one and solutions.
Sheet two and solutions.
Sheet three and solutions.
Sheet four and solutions.
Sheet five and solutions.
Sheet six and solutions.
C. Hadlock, Field theory and its classical problems
I. Stewart, Galois Theory
J. Rotman, Galois Theory
J. Fraleigh, A first course in abstract algebra
I. Herstein, Topics in algebra
I personally bought this book when I was an undergraduate:
D. J. H. Garling, A course in Galois Theory
but actually I learnt Galois theory from my lecture notes, so perhaps I'm not the best person to ask about books.