  We present an algebraic approach to string theory. An embedding of $sl(2|1)$
in a super Lie algebra together with a grading on the Lie algebra determines a
nilpotent subalgebra of the super Lie algebra. Chirally gauging this subalgebra
in the corresponding Wess-Zumino-Witten model, breaks the affine symmetry of
the Wess-Zumino-Witten model to some extension of the $N=2$ superconformal
algebra. The extension is completely determined by the $sl(2|1)$ embedding. The
realization of the superconformal algebra is determined by the grading. For a
particular choice of grading, one obtains in this way, after twisting, the BRST
structure of a string theory. We classify all embeddings of $sl(2|1)$ into Lie
super algebras and give a detailed account of the branching of the adjoint
representation. This provides an exhaustive classification and characterization
of both all extended $N=2$ superconformal algebras and all string theories
which can be obtained in this way.
