Abstract
In this dissertation, we enumerate the 27 lines on a smooth cubic surface X ⊂ P3. We
do this by understanding the combinatorics of the subset S of disjoint lines on X of the
Grassmanian Gr(2,4) of lines on P3. Further, using the incidence correspondence de�ned
by the projection (X, �) �→ X where � is a line on X, we show that the relation is a 27-
sheeted covering map by studying the inverse image of lines on a smooth cubic X under
the blowup map
B�6 : B�6P2 ��� X.