Galois theory is a central part of algebra, dealing with symmetries between solutions of algebraic equations in one variable. This is a collection of papers from the participants of a conference on Galois theory, and brings together articles from some of the world's leading experts in this field. Topics are centred around the Inverse Galois Problem, comprising the full range of methods and approaches in this area, making this an invaluable resource for all those whose research involves Galois theory.

• Indispensable for researchers in this area • Authors are top names • Exciting area

### Contents

1. Galois theory of semilinear transformations S. Abhyankar; 2. Some arithmetic properties of algebraic covers P. Debes; 3. Tools for the computation of algebraic covers J.-M. Couveignes; 4. Infinite towers of unramified curve covers defined over a number field G. Frey, E. Kani and H. Volklein; 5. Modular towers of noncongruence curves M. Fried; 6. Embedding problems and adding branch points D. Harbater; 7. On beta and gamma functions associated with the Grothendieck–Teichmüller group Y. Ihara; 8. Arithmetically exceptional functions and elliptic curves P. Mueller; 9. Tangential base points and Eisenstein power series H. Nakamura; 10. Braid-abelian tuples in Sp(p,n) J. G. Thompson and H. Volklein.

### Reviews

' … an invaluable resource for all those whose research involves Galois theory.' Extrait de L'Enseignement Mathématique

'… a volume with interesting methods, examples, attempts and seminal ideas around the Inverse Galois theory; full of ideas, and nice to read.' Niew Archief voor Wiskunde