  The aim of these notes is to explain the remarkable formula found by Yau and
Zaslow to express the number of rational curves on a K3 surface. Projective K3
surfaces fall into countably many families F(g) (g>0); a surface in F(g) admits
a g-dimensional linear system of curves of genus g. Such a system contains a
positive number, say n(g), of rational (highly singular) curves. The formula is
\sum n(g) q^g = q/D((q), where D(q) = q \prod (1-q^n)^{24} is the well-known
modular form of weight 12.
