This volume of invited articles by several outstanding mathematicians in algebra, algebraic geometry, and number theory is dedicated to Vladimir Drinfeld on the occasion of his 50th birthday. These surveys and original research articles broadly reflect the range of Drinfeld's work in these areas, especially his profound contributions to the Langlands program and mathematical physics. The contributors include: V.V. Fock, E. Frenkel, D. Gaitsgory, A.B. Goncharov, E. Hrushovski, Y. Ihara, D. Kazhdan, M. Kisin, I. Krichever, G. Laumon, Yu. Manin, and V. Schechtmann.

"The book is largely self-contained...There is a nice introduction to symplectic geometry and a charming exposition of equivariant K-theory. Both are enlivened by examples related to groups...An attractive feature is the attempt to convey some informal 'wisdom' rather than only the precise definitions. As a number of results are] due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory...it has already proved successful in introducing a new generation to the subject." (Bulletin of the AMS)