We classify (2,2) supersymmetric string vacua which are represented as
Landau-Ginzburg theories, with a quasihomogeneous potential that has
an isolated singularity at the origin. There are at least three thousa
nd distinct models in this class, All vacua of this type lead to Euler
numbers lying in the range -960 less-than-or-equal-to X less-than-or-
equal-to 960. The Euler characteristics do not pair up completely; hen
ce 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 mani
folds and describe a subtlety regarding Landau-Ginzburg potentials wit
h an arbitrary number of fields. We also show that the use of topologi
cal identities makes it possible to relate Landau-Ginzburg theories to
types of Calabi-Yau manifolds for which the usual Landau-Ginzburg fra
mework does not apply.