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b'This thesis presents inclusive $e^\\\\pm p$ single and double differential cross\\nsections for neutral current deep inelastic scattering measured as functions of\\nthe four-momentum transfer squared $Q^2$ and the Bjorken variable $x$ in\\ninteractions of longitudinally polarised leptons with unpolarised protons using\\nthe H1 detector at HERA~II. An overview of the phenomenology of deep inelastic\\nscattering is given and the experimental apparatus as well as the measurement\\nand analysis procedures are described. The analysis is based on $e^+p$ data\\ntaken in 2003-04 and $e^-p$ data taken in 2005 at a centre-of-mass energy of\\n$\\\\sqrt s = 318$~GeV, with integrated luminosities of 47.6~pb$^{-1}$ and\\n98.4~pb$^{-1}$ for the $e^+ p$ and $e^- p$ samples, respectively. The cross\\nsections are measured in the range of $200 < Q^2 < 20\\\\,000$~GeV$^2$ and\\n$0.0032<0.65$. The measurements are used to study polarisation effects in\\nneutral current interactions and to determine the structure function\\n$x\\\\tilde{F}_3$. The new HERA~II data are combined together with previously\\npublished data from HERA~I to determine the structure function $x\\\\tilde{F}_3$\\nwith improved precision. Furthermore, this measurement is combined with the\\ncorresponding ZEUS measurement to provide the most accurate measurement of the\\ninterference structure function $xF_3^{\\\\gamma Z}$, which is sensitive to the\\nvalence quark distributions down to low values of $x$. The data on polarised\\ncross section asymmetries $A^\\\\pm$ are also combined with the ZEUS data. This\\nleads to the first observation of parity violation in neutral current $e^\\\\pm p$\\nscattering at distances down to $10^{-18}$~m. The data are well described by\\nthe Standard Model predictions.'