  We consider the bosonic sectors of supergravity theories in ten and eleven
dimensions which correspond to the low energy limits of string theories and
M-theory. The solutions of supergravity field equations are known as
supergravity backgrounds and the number of preserved supersymmetries in those
backgrounds are determined by Killing spinors. We provide some examples of
supergravity backgrounds which preserve different fractions of supersymmetry.
An important invariant for the characterization of supergravity backgrounds is
their Killing superalgebras which are constructed out of Killing vectors and
Killing spinors of the background. After constructing Killing superalgebras of
some special supergravity backgrounds, we discuss about the possibilities of
the extensions of these superalgebras to include the higher degree hidden
symmetries of the background.
