## ABSTRACT

To complete the construction of a four-dimensional theory it is necessary next to compactify six of the ten dimensions in some way for both right and left movers. The simplest possibility is a toroidal compactification. A somewhat different approach to the construction of four-dimensional heterotic string theories is to return to the original heterotic string with the right movers of a superstring in ten dimensions and the uncompactified left movers of a bosonic string in sixteen dimensions, and to reduce the number of space-time dimensions to four directly by fermionizing all other string degrees of freedom. A simple modification of toroidal compactification is compactification on an orbifold, a six-dimensional space obtained by identifying points on the torus that are mapped into one another by certain discrete symmetries of the lattice of the torus, referred to as the point group.