Consistent perturbation theory for thermodynamical quantities in type II superconductors in magnetic field at low temperatures is developed. It is complementary to the existing expansion valid at high temperatures. Magnetization and specific heat are calculated to two loop order and compare well to existing Monte Carlo simulations and experiments. Typeset using REVTEX 1 Thermal fluctuations play much larger role in high Tc superconductors then in the low temperature ones because the Ginzburg parameter Gi characterizing fluctuations is much larger. In the presence of magnetic field the importance of fluctuations in high Tc superconductors is further enhanced. Strong magnetic field effectively suppresses long wavelength fluctuations in direction perpendicular to the field reducing dimensionality of the fluctuations by two . Under these circumstances fluctuations influence various physical properties and even lead to new observable qualitative phenomena like vortex lattice melting into vortex liquid far below the mean field phase transition line. It is quite straightforward to systematicall
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