Progress in Galois Theory : Proceedings of John Thompson's 70th Birthday Conference (Developments in Mathematics Vol.12) (2004. X, 168 p.)

The legacy of Galois was the beginning of Galois theory as well as group theory. The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the 'Inverse Problem of Galois Theory').