He introduced the relativistically invariant Mandelstam variables into particle physics in 1958 as a convenient coordinate system for formulating his double dispersion relations.
[1] The double dispersion relations were a central tool in the bootstrap program which sought to formulate a consistent theory of infinitely many particle types of increasing spin.
He used the conformal invariance to calculate tree level string amplitudes on many worldsheet domains.
In quantum field theory, Mandelstam and independently Sidney Coleman extended work of Tony Skyrme to show that the two dimensional quantum Sine-Gordon model is equivalently described by a Thirring model whose fermions are the kinks.
Among his students at Berkeley are Joseph Polchinski, Michio Kaku, Charles Thorn and Hessamaddin Arfaei.