  The knowledge of {\it non usual} and sometimes {\it hidden} symmetries of
(classical) integrable systems provides a very powerful setting-out of
solutions of these models. Primarily, the understanding and possibly the
quantisation of intriguing symmetries could give rise to deeper insight into
the nature of field spectrum and correlation functions in quantum integrable
models. With this perspective in mind we will propose a general framework for
discovery and investigation of local, quasi-local and non-local symmetries in
classical integrable systems. We will pay particular attention to the structure
of symmetry algebra and to the r\^ole of conserved quantities. We will also
stress a nice unifying point of view about KdV hierarchies and Toda field
theories with the result of obtaining a Virasoro algebra as exact symmetry of
Sine-Gordon Model.
