  In the framework of the Cartan classification of Hamiltonians, a kind of
topological classification of Fermi surfaces is established in terms of
topological charges. The topological charge of a Fermi surface depends on its
codimension and the class to which its Hamiltonian belongs. It is revealed that
six types of topological charges exist, and they form two groups with respect
to the chiral symmetry, with each group consisting of one original charge and
two descendants. It is these nontrivial topological charges which lead to the
robust topological protection of the corresponding Fermi surfaces against
perturbations that preserve discrete symmetries.
