  Classical Lie group theory provides a universal tool for calculating symmetry
groups for systems of differential equations. However Lie's method is not as
much effective in the case of integral or integro-differential equations as
well as in the case of infinite systems of differential equations. This paper
is aimed to survey the modern approaches to symmetries of integro-differential
equations. As an illustration, an infinite symmetry Lie algebra is calculated
for a system of integro-differential equations, namely the well-known Benney
equations. The crucial idea is to look for symmetry generators in the form of
canonical Lie-Backlund operators.
