Content （1） Intro to elliptic curves over global, local and global fields explain the invariants that appears in the BSD formula;L-functions of elliptic curves; Galois cohomology of elliptic curves; Tate shafarevich groups；Finally the statement of the BSD. （2） Survey on the results so far regarding BSD （3） Computational methods (this lecture you can give), modular symbols etc... （4） p-adic analogue of the BSD （5） Computation regarding the p-adic BSD （6） Generalizations to abelian varieties