  We propose an entirely new class of particle physics models of inflation
based on the phase transition associated with the spontaneous breaking of
family symmetry responsible for the generation of the effective quark and
lepton Yukawa couplings. We show that the Higgs fields responsible for the
breaking of family symmetry, called flavons, are natural candidates for the
inflaton field in new inflation, or the waterfall fields in hybrid inflation.
This opens up a rich vein of possibilities for inflation, all linked to the
physics of flavour, with interesting cosmological and phenomenological
implications. Out of these, we discuss two examples which realise flavon
inflation: a model of new inflation based on the discrete non-Abelian family
symmetry group A_{4} or Delta_{27}, and a model of hybrid inflation embedded in
an existing flavour model with a continuous SU(3) family symmetry. With the
inflation scale and family symmetry breaking scale below the Grand Unification
Theory (GUT) scale, these classes of models are free of the monopole (and
similar) problems which are often associated with the GUT phase transition.
