By Tamás Szamuely

Ever because the techniques of Galois teams in algebra and primary teams in topology emerged in the course of the 19th century, mathematicians have identified of the powerful analogies among the 2 suggestions. This publication provides the relationship beginning at an straight forward point, displaying how the really appropriate use of algebraic geometry supplies entry to the robust interaction among algebra and topology that underpins a lot glossy examine in geometry and quantity idea. Assuming as little technical historical past as attainable, the publication starts off with uncomplicated algebraic and topological options, yet already provided from the trendy point of view recommended by way of Grothendieck. this permits a scientific but available improvement of the theories of basic teams of algebraic curves, basic teams of schemes, and Tannakian basic teams. the relationship among basic teams and linear differential equations is usually constructed at expanding degrees of generality. Key functions and up to date effects, for instance at the inverse Galois challenge, are given all through.