The book originated from a major course of lectures on Supersymmetry and Supergravity at the SERC School in Theoretical High Energy Physics held at Bangalore in 1986 and from lectures at Institute of Physics, Bhubaneswar. It aims at presenting the basic materials of the subject in a compact form and would be useful to gaduate students as well as to other researchers. Topics such a heterotic string theory as well as compactification of higher dimensional spaces as related to Supersymmetry and Supergravity are included, along with appendices on differential geometry and applications to group theory. Besides symmetries, some dynamical quations like quantum description of phase transition has also been dealt with.