  Basic notions regarding classical integrable systems are reviewed. An
algebraic description of the classical integrable models together with the zero
curvature condition description is presented. The classical r-matrix approach
for discrete and continuum classical integrable models is introduced. Using
this framework the associated classical integrals of motion and the
corresponding Lax pair are extracted based on algebraic considerations. Our
attention is restricted to classical discrete and continuum integrable systems
with periodic boundary conditions. Typical examples of discrete (Toda chain,
discrete NLS model) and continuum integrable models (NLS, sine-Gordon models
and affine Toda field theories) are also discussed.
