  This is a revised version of the notes from the week-long course I gave at
the Centre de Recerca Matematica, Barcelona, in September of 2010. The aim is
to give a working overview of recent methods and results in "Blaschkean
integral geometry" (i.e. the subject revolving around the kinematic formulas of
Blaschke) in the wake of the revolutionary new methods introduced over the past
ten years or so by S. Alesker. The most striking new feature is the extent to
which the subject has been invaded by algebra.
