  It is well established that the physical phenomenon of intermittency can be
investigated via the spectral analysis of a transfer operator associated with
the dynamics of an interval map with indifferent fixed point. We present here
for the first time a complete spectral analysis for an example of such an
intermittent map, the Farey map. We give a simple proof that the transfer
operator is self-adjoint on a suitably defined Hilbert space and show that its
spectrum decomposes into a continuous part (the interval $[0,1]$) and isolated
eigenvalues of finite multiplicity. Using a suitable first-return map, we
present a highly efficient numerical method for the determination of all the
eigenvalues, including the ones embedded in the continuous spectrum.
