Diophantine Geometry is a very old and fascinating field. It deals with entire or rational
solutions of polynomial equations. A famous example is Fermat's conjecture which was open for many
years until Wiles solved it. In Diophantine Geometry II, we will study local heights and then prove
the Mordell-conjecture. We will follow Vojta's proof with simplification of Bombieri. This proof is
more elementary than the original proof of Faltings for which Faltings received the Fields medal in
1986.