Gabriel Navarro is Professor in the Department of Mathematics at the University of Valencia. He has published over 160 papers, and the widely-cited volume Characters and Blocks of Finite Groups (Cambridge, 1998). He is a leading researcher in character theory and the McKay conjecture.

'Navarro continues his informative preface with an exhaustive overview of the work done on this conjecture, and he includes a number of fascinating insights and elaborations.' Michael Berg, MAA Reviews

• Preface; Notation; 1. The basics; 2. Action on characters by automorphisms; 3. Galois action on characters; 4. Character values and identities; 5. Characters over a normal subgroup; 6. Extension of characters; 7. Degrees of characters; 8. The Howlett–Isaacs theorem; 9. Global-local counting conjectures; 10. A reduction theorem for the McKay conjecture; Appendix; Bibliographic notes; References; Index.