  We present a class of N=1 supersymmetric models of particle physics, derived
directly from heterotic M-theory, that contain three families of chiral quarks
and leptons coupled to the gauge group $SU(3)_C\times SU(2)_{L}\times
U(1)_{Y}$. These models are a fundamental form of ``brane-world'' theories,
with an observable and hidden sector each confined, after compactification on a
Calabi-Yau threefold, to a BPS threebrane separated by a five-dimensional bulk
space with size of the order of the intermediate scale. The requirement of
three families, coupled to the fundamental conditions of anomaly freedom and
supersymmetry, constrains these models to contain additional fivebranes wrapped
around holomorphic curves in the Calabi-Yau threefold. These fivebranes
``live'' in the bulk space and represent new, non-perturbative aspects of these
particle physics vacua. We discuss, in detail, the relevant mathematical
structure of a class of torus-fibered Calabi-Yau threefolds with non-trivial
first homotopy groups and construct holomorphic vector bundles over such
threefolds, which, by including Wilson lines, break the gauge symmetry to the
standard model gauge group. Rules for constructing phenomenological particle
physics models in this context are presented and we give a number of explicit
examples.
