This
note explains the following topics: Plane Curves, Rational Points on
Plane Curves, The Group Law on a Cubic Curve, Functions on Algebraic Curves and
the Riemann-Roch Theorem, Reduction of an Elliptic Curve Modulo p, Elliptic
Curves over Qp, Torsion Points, Neron Models, Elliptic Curves over the Complex
Numbers, The Mordell-Weil Theorem: Statement and Strategy, The Tate-Shafarevich
Group; Failure Of The Hasse Principle, Elliptic Curves Over Finite Fields, The
Conjecture of Birch and Swinnerton-Dyer, Elliptic Curves and Sphere Packings,
The Conjecture of Birch and Swinnerton-Dyer, Algorithms for Elliptic Curves.

**Author(s):** J.S. Milne

163**Pages**