This is an expository introduction to fusion rules for affine Kac-Moody
algebras, with major focus on the algorithmic aspects of their computation and
the relationship with tensor product decompositions. Many explicit examples are
included with figures illustrating the rank 2 cases. New results relating
fusion coefficients to tensor product coefficients are proved, and a conjecture
is given which shows that the Frenkel-Zhu affine fusion rule theorem can be
seen as a beautiful generalization of the Parasarathy-Ranga Rao-Varadarajan
tensor product theorem. Previous work of the author and collaborators on a
different approach to fusion rules from elementary group theory is also
explained.Comment: 43 pp, LateX, 18 postscript figures. Paper for my talk at the
Ramanujan International Symposium on Kac-Moody Lie Algebras and Applications,
ISKMAA-2002, Jan. 28-31, 2002, Chennai, India. Important references and
comments added. Final version accepted for publication. Also available from
ftp://ftp.math.binghamton.edu/pub/alex/Madras_Paper_Latex.ps.g
