The lectures in these proceedings discuss topics in areas including: statistical mechanics; the geometric and algebraic approaches to q-deformation theories; and 2-dimensional gravity and related problems of mathematical physics, including Vassiliev invariants and the Jones polynomials.

Vassiliev invariants and the Jones polynomials, L. Kauffman; lectures on quantum groups - representations and duality, V.K. Dobrev; aspects of yangian invariant factorized s-matrices, N.J. MacKay; beyond supersymmetry and quantum symmetry, S. Majid; infinite dimensional R matrix with complete Z symmetry, Y. Shibukawa, K. Ueno; Goryacher-Chaplygin top at a complex coupling constant, I.V. Komarov; on representation theories of Iwanori-Hecke algebras Hq(W) at roots q of unity, H. Yamane; q-deformation of the conformal algebra, Z. Popowicz. (Part contents).