In the setting of the geometric Langlands program, it is conjectured that kernels which should give rise to Langlands functoriality, and relations between values of L-functions and some periods, exist. Some cases are known (e.g. the geometric theta correspondence and the geometrization of Rankin-Selberg integrals, due to Lysenko), the rest is mainly conjectural. However the (partly conjectural) classical limits may be described and their properties studied. In the first hour I will recall some elementary facts of symplectic geometry and the classical limit of the Langlands correspondence via the Hitchin fibration.