  In six spacetime dimensions, the heterotic string is dual to a Type $IIA$
string. On further toroidal compactification to four spacetime dimensions, the
heterotic string acquires an $SL(2,\BbbZ)_S$ strong/weak coupling duality and
an $SL(2,\BbbZ)_T \times SL(2,\BbbZ)_U$ target space duality acting on the
dilaton/axion, complex Kahler form and the complex structure fields $S,T,U$
respectively. Strong/weak duality in $D=6$ interchanges the roles of $S$ and
$T$ in $D=4$ yielding a Type $IIA$ string with fields $T,S,U$. This suggests
the existence of a third string (whose six-dimensional interpretation is more
obscure) that interchanges the roles of $S$ and $U$. It corresponds in fact to
a Type $IIB$ string with fields $U,T,S$ leading to a four-dimensional
string/string/string triality. Since $SL(2,\BbbZ)_S$ is perturbative for the
Type $IIB$ string, this $D=4$ triality implies $S$-duality for the heterotic
string and thus fills a gap left by $D=6$ duality. For all three strings the
total symmetry is $SL(2,\BbbZ)_S \times O(6,22;\BbbZ)_{TU}$. The
$O(6,22;\BbbZ)$ is {\it perturbative} for the heterotic string but contains the
conjectured {\it non-perturbative} $SL(2,\BbbZ)_X$, where $X$ is the complex
scalar of the $D=10$ Type $IIB$ string. Thus four-dimensional triality also
provides a (post-compactification) justification for this conjecture. We
interpret the $N=4$ Bogomol'nyi spectrum from all three points of view. In
particular we generalize the Sen-Schwarz formula for short multiplets to
include intermediate multiplets also and discuss the corresponding black hole
spectrum both for the $N=4$ theory and for a truncated $S$--$T$--$U$ symmetric
$N=2$ theory. Just as the first two strings are described by the
four-dimensional {\it elementary} and {\it dual solitonic} solutions, so the
