Understanding the structure of the set of rational points on an elliptic curve - essentially a cubic equation - has been an aim in number theory for over a century. It has connections to open problems buried in antiquity, such as the congruent number problem. The Birch and Swinnerton-Dyer (BSD) conjecture, a Clay millennium problem, predicts a mystifying interrelation among the rational points and the associated L-function. The Bloch-Kato conjecture is a vast generalisation of the BSD conjecture. Over the last decade, the BSD has witnessed notable progress.In this precursor to the upcoming program on the recent progress, a series of mini-courses is intended mainly as an introduction to some of the breakthroughs towards the BSD conjecture from the mid 1970's - the early 1990's; namely after: Coates-Wiles, Gross-Zagier and Kolyvagin, Kato. An introduction to recent progress towards the Gross-Stark conjecture will also appear.List of speakers and mini courses for the online precursor:He...
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