Introduced by Borel in the late 1950's, equivariant cohomology encodes
information about how the topology of a space interacts with a group
action.  Quite some time passed before algebraic geometers picked up on
these ideas, but in the last twenty years, equivariant techniques have
found many applications in enumerative geometry, Gromov-Witten theory,
and the study of toric varieties and homogeneous spaces.  In fact, many
classical algebro-geometric notions, going back to the degeneracy locus
formulas of Giambelli, are naturally statements about certain
equivariant cohomology classes.

These lectures will survey some of the main features of equivariant
cohomology at an introductory level.  The first part will be an
overview, including basic definitions and examples.  In the second
lecture, I will discuss one of the most useful aspects of the theory:
the possibility of localizing at fixed points without losing
information.  The third lecture will focus on Grassmannians and other
homogeneous spaces, and describe some recent "positivity" results about
their equivariant cohomology rings.