Interactions of Strings Compactified on Orbifolds.

It is very important to understand the process of string compactification before one can extract any reliable phenomenology. We consider an exactly solvable method of string compactification, in which the internal space is an orbifold. We compute various interaction amplitudes and describe how other amplitudes can be calculated. Multi-valued string variables are handled by formulating the amplitudes on covering spaces where they become single -valued. In the computation of the amplitudes, stretched string intermediate states give rise to expressions that are non-perturbative from the non-linear sigma model point of view. We also discuss, in the context of Z orbifold, the 'blowing up' of the fixed points of an orbifold, to give rise to a Calabi-Yau manifold. The resulting Calabi -Yau manifold is shown to be non-perturbatively stable.