The phase diagram of a layered superconductor in a large parallel magn
etic field is calculated. This includes a calculation of the lower cri
tical field beyond which the superconductor is in the FFLO-state and p
ossesses a spatially modulated order parameter and spin polarization.
The order parameter, spin polarization, free-energy density, and phase
boundaries of this unconventional superconducting phase are evaluated
numerically in the complete B - T plane. The analysis suggests that t
he transition at the lower critical field is of second order, and not
of first order, as previously assumed. The order parameter of the FFLO
-state merges continuously into the uniform superconducting state.