  The Landau expansion for the free energy of the superconducting mixed state
near the upper critical field in powers of the square modulus of the order
parameter averaged over Abrikosov lattice is derived.
  The analytical calculations has been carried out in frame of Gor'kov
formalism for 3-dimensional isotropic BCS model beyond the limits of
quasiclassical approximation, another words with Landau quantization of the
quasiparticle energy levels taken into consideration. The derivation is
performed at low temperature and high enough but finite crystal's purity.
  The effect of Pauli paramagnetic terms is taken into account. The quantum
oscillations of the critical temperature, the order parameter's amplitude and
the magnetization (de Haas-van Alphen effect) in the mixed state are found. The
limitation of validity of a mean field approach due to critical fluctuations
(Ginzburg criterion) for the phase transition under consideration is
established.
