Edward Frenkel is Professor of Mathematics at the University of California, Berkeley

'This book is well written and will give especially the interested student, an excellent basis in this rapidly developing area of mathematics. For those beyond the level of student it also provides very useful text to follow, and perhaps to participate, in these developments.' Samuel James Patterson, Zentralblatt MATH

• Preface; 1. Local Langlands Correspondence; 2. Vertex algebras; 3. Constructing central elements; 4. Opers and the center for a general Lie algebra; 5. Free field realization; 6. Wakimoto modules; 7. Intertwining operators; 8. Identification of the center with functions on opers; 9. Structure of bg-modules of critical level; 10. Constructing the local Langlands Correspondence; Appendix; References.

Edward Frenkel is Professor of Mathematics at the University of California, Berkeley

'This book is well written and will give especially the interested student, an excellent basis in this rapidly developing area of mathematics. For those beyond the level of student it also provides very useful text to follow, and perhaps to participate, in these developments.' Samuel James Patterson, Zentralblatt MATH

• Preface; 1. Local Langlands Correspondence; 2. Vertex algebras; 3. Constructing central elements; 4. Opers and the center for a general Lie algebra; 5. Free field realization; 6. Wakimoto modules; 7. Intertwining operators; 8. Identification of the center with functions on opers; 9. Structure of bg-modules of critical level; 10. Constructing the local Langlands Correspondence; Appendix; References.