This volume contains the expanded versions of the lectures given by the
authors at the C.I.M.E. instructional conference held in Cetraro, Italy,
from July 12 to 19, 1997. The papers collected here are broad surveys of
the current research in the arithmetic of elliptic curves, and also
contain several new results which cannot be found elsewhere in the
literature. Owing to clarity and elegance of exposition, and to the
background material explicitly included in the text or quoted in the
references, the volume is well suited to research students as well as to
senior mathematicians.