  We investigate a class of (2,2) supersymmetric string vacua which may be
represented as Landau--Ginzburg theories with a quasihomogeneous potential
which has an isolated singularity at the origin. There are at least three
thousand distinct models in this class. All vacua of this type lead to Euler
numbers which lie in the range $-960 \leq \chi \leq 960$. The Euler
characteristics do not pair up completely hence the space of Landau--Ginzburg
ground states is not mirror symmetric even though it exhibits a high degree of
symmetry. We discuss in some detail the relation between Landau--Ginzburg
models and Calabi--Yau manifolds and describe a subtlety regarding
Landau--Ginzburg potentials with an arbitrary number of fields. We also show
that the use of topological identities makes it possible to relate
Landau-Ginzburg theories to types of Calabi-Yau manifolds for which the usual
Landau-Ginzburg framework does not apply.
