  The construction of mirror symmetry in the heterotic string is reviewed in
the context of Calabi-Yau and Landau-Ginzburg compactifications. This framework
has the virtue of providing a large subspace of the configuration space of the
heterotic string, probing its structure far beyond the present reaches of
solvable models. The construction proceeds in two stages: First all
singularities/catastrophes which lead to ground states of the heterotic string
are found. It is then shown that not all ground states described in this way
are independent but that certain classes of these LG/CY string vacua can be
related to other, simpler, theories via a process involving fractional
transformations of the order parameters as well as orbifolding. This
construction has far reaching consequences. Firstly it allows for a systematic
identification of mirror pairs that appear abundantly in this class of string
vacua, thereby showing that the emerging mirror symmetry is not accidental.
This is important because models with mirror flipped spectra are a priori
independent theories, described by distinct CY/LG models. It also shows that
mirror symmetry is not restricted to the space of string vacua described by
theories based on Fermat potentials (corresponding to minimal tensor models).
Furthermore it shows the need for a better set of coordinates of the
configuration space or else the structure of this space will remain obscure.
While the space of LG vacua is {\it not} completely mirror symmetric, results
described in the last part suggest that the space of Landau--Ginburg {\it
orbifolds} possesses this symmetry.

High Energy Physics - Theory