  We study the construction of Hermitian Yang-Mills instantons over resolutions
of Calabi-Yau cones of arbitrary dimension. In particular, in d complex
dimensions, we present an infinite family, parametrised by an integer k and a
continuous modulus, of SU(d) instantons. A detailed study of their properties,
including the computation of the instanton numbers is provided. We also explain
how they can be used in the construction of heterotic non-Kahler
compactifications.
