  In the 1980's, work of Green and Lazarsfeld helped to uncover the beautiful
interplay between the geometry of the embedding of a curve and the syzygies of
its defining equations. Similar results hold for the first secant variety of a
curve, and there is a natural conjectural picture extending to higher secant
varieties as well. We present an introduction to the algebra and geometry used
in previous work of the authors to study syzygies of secant varieties of curves
with an emphasis on examples of explicit computations and elementary cases that
illustrate the geometric principles at work.
