Developments in mathematical physics during the second half of the 20th century influenced a number of mathematical areas, among the more significant being representation theory, differential equations, combinatorics, and algebraic geometry. In all areas, the dynamic role of integrable models has been central. This volume focuses on the ongoing importance of integrability in: conformal field theory, massive quantum field theory, solvable lattice models, quantum affine algebras, the Painleve equations and combinatorics. Will serve as an excellent reference text for mathematical physicists and graduate students.