  We give a summary of R. Borcherds' solution (with some modifications) to the
following part of the Conway-Norton conjectures: Given the Monster simple group
and Frenkel-Lepowsky-Meurman's moonshine module for the group, prove the
equality between the graded characters of the elements of the Monster group
acting on the module (i.e., the McKay-Thompson series) and the modular
functions provided by Conway and Norton. The equality is established using the
homology of a certain subalgebra of the monster Lie algebra, and the
Euler-Poincare identity.
