  We discuss the Noether Symmetry Approach in the framework of Gauss-Bonnet
cosmology showing that the functional form of the $F(R, {\cal G})$ function,
where $R$ is the Ricci scalar and ${\cal G}$ is the Gauss-Bonnet topological
invariant, can be determined by the presence of symmetries. Besides, the method
allows to find out exact solutions due to the reduction of cosmological
dynamical system and the presence of conserved quantities. Some specific
cosmological models are worked out
