Abstract : This Report summarizes the results of the first 10 months' activities of the LHC Higgs Cross Sections Working Group. The main goal of the working group was to present the status-of-art on Higgs Physics at the LHC integrating all new results that have appeared in the last few years. The Report is more than a mere collection of the proceedings of the general meetings. The subgroups have been working in different directions. An attempt has been made to present the first Report from these subgroups in a complete and homogeneous form. The subgroups' contributions correspondingly comprise the main parts of the Report. A significant amount of work has been performed in providing higher-order corrections to the Higgs-boson cross sections and pinning down the theoretical uncertainty of the Standard Model predictions. This Report comprises explicit numerical results on total cross sections, leaving the issues of event selection cuts and differential distributions to future publications. The subjects for further study are identified.