The specific heat C of a sintered polycrystalline sample of MgB2 with a bulk superconducting transition temperature Tc=36.7 K is measured as a function of the temperature (2-300 K) and magnetic field (0-16 T), together with magnetic properties (normal-state susceptibility, superconducting state magnetization, etc.). The Sommerfeld constant gamma=0.89+-0.05 mJ/K^2/gat (2.7 mJ/K^2/mol) is determined in the normal state above Hc2. The normal- and superconducting state entropies are equal at Tc. Several moments of the phonon density of states are obtained from the lattice specific heat. We report bulk values for: the thermodynamic critical field, the slope of the upper critical field, the Ginzburg-Landau parameter, the coherence length, the lower critical field, the London penetration depth. These results characterize MgB2 as a type-II superconductor. The nearly quadratic dependence of C(T) versus T at T<<Tc, its non-linear field dependence, and the discrepancy between the electron-phonon coupling constant lambda_ep as determined by the renormalization of the electron density-of-states (lambda_ep=0.6) and by McMillans equation for isotropic superconductors (lambda_ep=1.1), are inconsistent with a single isotropic gap. In addition to high phonon frequencies, anisotropy or two-band gap structure may explain why the critical temperature of this superconductor is high in spite of its low condensation energy, which does not exceed 1/16 of that of YBa2Cu3O7 and 1/4 of that of Nb3Sn.
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