In this introductory talk, we present the Birch and Swinnerton-Dyer conjecture, survey some of the results that provide evidence about its veracity, and mention a generalization by Beilinson, Bloch and Kato.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/158