  This paper is based on author's lectures at Kyoto University in 2010 Summer,
and in the 6th MSJ-SI `Development of Moduli Theory' at RIMS in June 2013.
  The purpose of lectures was to review several results on Hilbert schemes of
points which were obtained after author's lecture note was written. Among many
results, we choose those which are about equivariant homology groups
$H^T_*(X^{[n]})$ of Hilbert schemes of points on the affine plane $X = \mathbb
C^2$ with respect to the torus action.
