  We consider generic properties of Lagrangians. Our main result is the Theorem
of Kupka-Smale, in the Lagrangian setting, claiming that, for a convex and
superlinear Lagrangian defined in a compact surface, for each $k\in
\mathbb{R}$, generically, in Ma\~n\'e's sense, the energy level, $k$, is
regular and all periodic orbits, in this level, are nondegenerate at all
orders, that is, the linearized Poincar\'e map, restricted to this energy
level, does not have roots of the unity as eigenvalues. Moreover, all
heteroclinic intersections in this level are transversal. All the results that
we present here are true in dimension $n \geq 2$, except one, whose proof we
are able to obtain just for dimension 2.
