Galois Groups and the Etale Fundamental Group

For all those undergrads who learned the Galois theory of covering spaces and always wondered what the link was to field extensions, I wrote up a very introductory-level exposition of exploring the rather deep link, eventually leading to an algebraic geometrical discussion on etale coverings of schemes, which intersects with topological covering space theory for Riemann surfaces, and is aesthetically similar enough for intuition from Galois theory and covering space theory to sniff out possible results. The construction is thanks to Grothendieck. The theory turns out to be quite fruitful having numerous applications to number theory and the inverse Galois problem. For a much more detailed discussion, one should look at Tamas Szamuley's "Galois Group and Covering Spaces." Enjoy, and feel free to post questions.