Spontaneous breaking of supersymmetry

There has been recently a revival of interest in supersymmetric gauge theories, stimulated by the hope that supersymmetry might help in clarifying some of the questions which remain unanswered in the so called Grand Unified Theories and in particular the gauge hierarchy problem. In a Grand Unified Theory one has two widely different mass scales: the unification mass M approx. = 10/sup 15/GeV at which the unification group (e.g. SU(5)) breaks down to SU(3) x SU(2) x U(1) and the mass ..mu.. approx. = 100 GeV at which SU(2) x U(1) is broken down to the U(1) of electromagnetism. There is at present no theoretical understanding of the extreme smallness of the ratio ..mu../M of these two numbers. This is the gauge hierarchy problem. This lecture attempts to review the various mechanisms for spontaneous supersymmetry breaking in gauge theories. Most of the discussions are concerned with the tree approximation, but what is presently known about radiative correction is also reviewed