  In the first part of the paper we give the denominator identity for all
simple finite-dimensional Lie super algebras $\frak g\/$ with a non-degenerate
invariant bilinear form. We give also a character and (super) dimension
formulas for all finite-dimensional irreducible $\frak g\/$-modules of
atypicality $\leq 1\/$ . In the second part of the paper we give the
denominator identity for the affine superalgebras $\hat{\frak g}\/$ associated
to $\frak g\/$. Specializations of this identity give almost all old and many
new formulas for the number of representations of an integer as sums of squares
and sums of triangular numbers. At the end, we introduce the notion of an
integrable $\hat{\frak g}\/$-module and give a classification of irreducible
integrable highest weight $\hat{\frak g}\/$-modules.
