In 13 lectures by three authors admittedly afflicted with " q -disease" (i.e. infatuation with the mathematical structures of conformal field theory and their q -deformations), they wax eruditely on this new area of theoretical physics and its powerful tools at the interface between mathematics and physics. Titles include: free field realization, quantum affine algebras, connection matrices for the quantum K-Z equations and elliptic functions, and current developments and future perspectives. Intended for those familiar with the representation theory of simple Lie algebras. Annotation c. by Book News, Inc., Portland, Or.