I'm supervising an undergraduate project on Galois theory and covering spaces.  I want to have him read about the fact that from a branched cover of a Riemann surface you get an extension of its field of meromorphic functions, and the Galois groups are the same, but I'm having trouble finding a good book.  Fulton's "Algebraic Topology" is OK but rushes through this point.  Forster's "Lectures on Riemann Surfaces" looks good but I'd rather not make him learn sheaves.  Any recommndations?