  This is an expanded and updated version of a lecture series I gave at Seoul
National University in September 1997. It is in some sense an update of the
1979 Griffiths and Harris paper with a similar title. I discuss:
  Homogeneous varieties, Topology and consequences Projective differential
invariants, Varieties with degenerate Gauss images, When can a uniruled variety
be smooth?, Dual varieties, Linear systems of bounded and constant rank, Secant
and tangential varieties, Systems of quadrics with tangential defects,
Recognizing uniruled varieties, Recognizing intersections of quadrics,
Recognizing homogeneous spaces, Complete intersections.
  This is a preliminary version, so please send me comments, corrections and
questions.
