  We study chaos in the Hamiltonian Mean Field model (HMF), a system with many
degrees of freedom in which $N$ classical rotators are fully coupled. We review
the most important results on the dynamics and the thermodynamics of the HMF,
and in particular we focus on the chaotic properties.We study the Lyapunov
exponents and the Kolmogorov--Sinai entropy, namely their dependence on the
number of degrees of freedom and on energy density, both for the ferromagnetic
and the antiferromagnetic case.
