  We present a study of the temperature-magnetic field phase diagram of
homogeneous and inhomogeneous superconductivity in the case of a
quasi-two-dimensional superconductor with an extended saddle point in the
energy dispersion under a parallel magnetic field. At low temperature, a huge
metastability region appears, limited above by a steep superheating critical
field (H_sh) and below by a strongly reentrant supercooling field (H_sc). We
show that the Pauli limit (H_p) for the upper critical magnetic field is
strongly enhanced due to the presence of the Van Hove singularity in the
density of states. The formation of a non-uniform superconducting state is
predicted to be very unlikely.
