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The microscopic superconductivity theory in MgB2 systems in the magneticfields directed parallel and perpendicular to the plane (ab) is built. The twoenergy bands of different dimensions overlapping on the Fermi surface(two-dimensional sigma- band and three-dimensional pi-band) are taken intoaccount. The theory is built taking into account the weak dispersion of theelectron energy of sigma -band in z direction. The systems of equations for thesuperconductive transition temperature Tc and the upper critical field Hc2(ab)are obtained. The analytic solutions of the equations for Hc2^0(ab) are foundin the two temperature areas: nearby the zero temperature T<<Tc^0 and in thevicinity of the superconductive transition temperature Tc^0-T<<Tc^0. Thetemperature dependencies of the upper critical fields Hc2(ab) and Hc2(c) on thetemperature are built, and the anisotropy coefficient gammaH=Hc2^0(ab)/Hc2^0(c)is determined. It is shown that the value of Hc2(ab) exceeds greatly the valueof Hc2(c) due to the system anisotropy (to small values of the average velocityof electrons in the crystallographic axis direction).

The microscopic theory of the upper critical field Hc2 in two-band  systems in the magnetic field directed parallel and perpendicular to the  plane (ab). Application to MgB2