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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.