  A brief, example-oriented introduction is given to special holonomy and its
uses in string theory and M-theory. We discuss A_k singularities and their
resolution; the construction of a K3 surface by resolving T^4/Z_2; holomorphic
cycles, calibrations, and worldsheet instantons; aspects of the low-energy
effective action for string compactifications; the significance of the standard
embedding of the spin connection in the gauge group for heterotic string
compactifications; G_2 holonomy and its relation to N=1 supersymmetric
compactifications of M-theory; certain isolated G_2 singularities and their
resolution; the Joyce construction of compact manifolds of G_2 holonomy; the
relation of D6-branes to M-theory on special holonomy manifolds; gauge symmetry
enhancement from light wrapped M2-branes; and chiral fermions from intersecting
branes. These notes are based on lectures given at TASI '01.
