  We consider an irreducible Anosov automorphism L of a torus T^d such that no
three eigenvalues have the same modulus. We show that L is locally rigid, that
is, L is C^1 conjugate to any C^1-small perturbation f with the same periodic
data. We also prove that toral automorphisms satisfying these assumptions are
generic in SL(d,Z). Examples constructed in the Appendix by Rafael de la Llave
show importance of the assumption on the eigenvalues.
