[en] The inclusive cross sections for both charged and neutral current processes have been measured in interactions of longitudinally polarized electrons (positrons) with unpolarized protons using the full data samples collected by H1 at HERA-II. The data taken at a center-of-mass energy of 319 GeV correspond to an integrated luminosity of 149.1 pb^-1 and 180.0 pb^-1 for e^-p and e⁺p collisions, representing an increase in statistics of a factor of 10 and 2, respectively, over the data from HERA-I. The measured double differential cross sections d²σ/dxdQ² cover more than two orders of magnitude in both Q², the negative four-momentum transfer squared, up to 30000 GeV², and Bjorken x, down to 0.003. The cross section data are compared to predictions of the Standard Model which is able to provide a good description of the data. The polarization asymmetry as a function of Q² is measured with improved precision, confirming the previous observation of P violation effect in neutral current ep scattering at distances down to 10^-18 m. The total cross sections of the charged current process, for Q² > 400 GeV² and inelasticity y < 0.9 are measured for 4 independent data samples with e^± beams and different polarization values. Together with the corresponding cross section obtained from the previously published unpolarized data, the polarization dependence of the charged current cross section is measured and found to be in agreement with the Standard Model prediction with the absence of right-handed charged current. The cross sections are combined with previously published data from H1 to obtain the most precise unpolarized measurements. These are used to extract the structure function xF₃^γZ which is sensitive to the valence quark distributions down to low x values. The new cross sections have also been used in a combined electroweak and QCD fit to significantly improve the light quark couplings to the Z-boson than those obtained based on the HERA-I data alone. (author)