  These are notes for a lecture series given at the Fields Institute Summer
School in Geometric Representation Theory and Extended Affine Lie Algebras,
held at the University of Ottawa in June 2009. We give an introduction to the
geometric realization of crystal graphs via the quiver varieties of Lusztig and
Nakajima. The emphasis is on motivating the constructions through concrete
examples. The relation between the geometric construction of crystals and
combinatorial realizations using Young tableaux is also discussed.
