The effect of fluctuations on the transport and thermodynamic properties of two-dimensional superconductors in a perpendicular magnetic field is studied at low temperature T ≪ T c 0 . The fluctuation conductivity is calculated in the framework of perturbation theory with the help of the usual diagram technique. It is shown that in the dirty case the Aslamazov-Larkin; Maki-Thompson; and density of states contributions are of the same order. At extremely low temperature T / T c 0 ≪[ H - H c 2 (0)]/ H c 2 (0) the total fluctuation correction to the normal conductivity is negative in the dirty limit and depends on the external magnetic field logarithmically δσ∝ln[ H - H c 2 (0)]. In the nonlocal clean limit; the Aslamazov-Larkin contribution to conductivity is evaluated with the aid of Helfand-Werthamer theory. The longitudinal and Hall conductivities are found. The fluctuating magnetization is calculated in the one-loop and two-loop approximations.