  We initiate the study of Brane Gas Cosmology (BGC) on manifolds with
non-trivial holonomy. Such compactifications are required within the context of
superstring theory in order to make connections with realistic particle
physics. We study the dynamics of brane gases constructed from various string
theories on background spaces having a K3 submanifold. The K3 compactifications
provide a stepping stone for generalising the model to the case of a full
Calabi-Yau three-fold. Duality symmetries are discussed within a cosmological
context. Using a duality, we arrive at an N=2 theory in four-dimensions
compactified on a Calabi-Yau manifold with SU(3) holonomy. We argue that the
Brane Gas model compactified on such spaces maintains the successes of the
trivial toroidal compactification while greatly enhancing its connection to
particle physics. The initial state of the universe is taken to be a small, hot
and dense gas of p-branes near thermal equilibrium. The universe has no initial
singularity and the dynamics of string winding modes allow three spatial
dimensions to grow large, providing a possible solution to the dimensionality
problem of string theory.
