  Inclusive e^\pm p single and double differential cross sections for neutral
(NC) and charged current (CC) deep inelastic scattering processes are measured
with the H1 detector at HERA. The data were taken at a centre-of-mass energy of
\sqrt{s} = 319 GeV with a total integrated luminosity of 327.8 pb^{-1} shared
between two lepton beam charges and two longitudinal lepton polarisation modes.
The differential cross sections are measured in the range of negative
four-momentum transfer squared, Q2, between 60 and 50 000 GeV2, and Bjorken x
between 0.0008 and 0.65. The measurements are combined with earlier published
unpolarised H1 data to improve statistical precision and used to determine the
structure function xF_3^{\gamma Z}. A measurement of the structure function
F_2^{\gamma Z}, sensitive to parity violating effects in NC, is presented for
the first time. The polarisation dependence of the CC total cross section is
also measured. The new measurements are well described by a next-to-leading
order QCD fit based on all published H1 inclusive cross section data which are
used to extract the parton distribution functions of the proton.
