(i) J. Silverman: The arithmetic of elliptic curves, Graduare Text in Math 106, Springer-Verlag.

(ii) A. Knapp: Elliptic Curves, Princeton Univ. Press, Mathematical Notes 40.

(iii) Shafarevich: Basic Algebraic Geometry I, 2nd Edition, Springer-Verlag.

(iv) R. Hartshorne: Algebraic Geometry, Springer-Verlag.

(v) Atiyah-MacDonald: Introduction to Commutative Algebra, Addison-Wesley

Week 1-2: Basic algebraic geometry ; Problem Sheet 1 (updated 1/26, Wed, 4pm)

Weeks 2-3: Algebraic Curves ; Problem Sheet 2 (updated 1/27, Thurs, 11pm)

Weeks 4-5: Geometry of Elliptic Curves ; Problem Sheet 3

Week 6-7: Elliptic Curves over Complex Numbers ; Problem Sheet 4 (coming soon)

Week 7: Elliptic Curves over non-algebraically closed fields (updated 2/22);

Week 8: Elliptic Curves over Finite and p-adic Fields (updated 3/2, 6pm); Problem Sheet 5 (coming soon)

Week 9-10: Elliptic Curves over Global Fields (updated 3/10, 10pm); Problem Sheet 6 (coming soon)