If you're interested, there is a beautiful book by Tamas Szamuely entitled Galois Groups and Fundamental Groups, which you can find herehere. It begins by looking at Galois groups, fundamental groups, and monodromy groups of Riemann surfaces (hence requiring only basic algebra, topology, and complex analysis) and the commonalities between them. It eventually generalizes all of this with Etale fundamental groups of schemes (this later section cites some results from commutative algebra and algebraic geometry).