  These notes cover our series of three lectures at Humboldt University in
Berlin for the October 2010 conference "Intersection theory on moduli space"
(organized by G. Farkas). The topic concerns relations among the kappa classes
in the tautological ring of the moduli space of genus g curves. After a
discussion of classical constructions in Wick form, we derive an explicit set
of relations obtained from the virtual geometry of the moduli space of stable
quotients. In a series of steps, the stable quotient relations are transformed
to simpler and simpler forms. Our final result establishes a previously
conjectural set of tautological relations proposed a decade ago by
Faber-Zagier.
  The Faber-Zagier relations are defined using g and a single series in one
variable with coefficients (6i)!/(3i)!(2i)!. Whether these relations span the
complete set of relations among the kappa classes on the moduli space of genus
g curves is an interesting question.
