The construction of affine Lie algebras by means of vertex operators has proved to be a remarkably fruitful line of research by motivating, being motivated by, and linking together a disparate range of sectors of mathematics and physics. Vertex operators entered mathematics through the work of J. Lepowsky and R. L. Wilson who gave an explicit construction of the affne algebra A’,l’ [LWl]. Their vertex operators were similar to ones used by physicists in the string model. Later on, I. Frenkel, V. Kac [FK], and G. Segal [S], found representations of afhne algebras using “untwisted” vertex operators. A large amount of very interesting research has followed stimulated by this observation and by the connection between classical combinatorial identities and the Weyl-Kac character formula [K, LM, LPl-2, LW2-4, Ma, Mil-21. A deeper understanding of vertex operators has been reached more recently as a result of work by Borcherds [B] who investigated general vertex operator algebras, and by Frenkel, Lepowsky, and A. Meurman in a series of papers, culminating in the recent book [FLM]. In particular, these three authors showed that the Monster finite simple group is the automorphism group of a certain vertex operator algebra, thus giving a natural realization of this largest among sporadic groups. This also established a surprising connection between the Monster and two-dimensional conformal quantum field theory, which is the physicists’ analogue of the theory of vertex operator algebras; cf. [BPZ, DL, FHL, FJ, TK, T, ZF, FLM].