  We present several pieces of evidence for strong-weak coupling duality
symmetry in the heterotic string theory, compactified on a six dimensional
torus. These include symmetry of the 1) low energy effective action, 2) allowed
spectrum of electric and magnetic charges in the theory, 3) allowed mass
spectrum of particles saturating the Bogomol'nyi bound, and 4) Yukawa couplings
between massless neutral particles and massive charged particles saturating the
Bogomol'nyi bound. This duality transformation exchanges the electrically
charged elementary string excitations with the magnetically charged soliton
states in the theory. It is shown that the existence of a strong-weak coupling
duality symmetry in four dimensional string theory makes definite prediction
about the existence of new stable monopole and dyon states in the theory with
specific degeneracies, including certain supersymmetric bound states of
monopoles and dyons. The relationship between strong-weak coupling duality
transformation in string theory and target space duality transformation in the
five-brane theory is also discussed. (Based on a talk given at the workshop on
Strings and Gravity, Madras, India.)
