For a subset D in an abelian group A, the subset
sum problem for D is to determine if D has a subset S which
sums to a given element of A. This is a well known NP-complete
problem, arising from diverse applications in coding theory,
cryptography and complexity theory. In this series of two
expository talks, we discuss and outline an emerging theory
of this subset sum problem by allowing D to have some
algebraic structure.