Molecular dynamics (MD) computer simulations of liquid water adsorbed on the muscovite (001) surface provide a greatly increased, atomistically detailed understanding of surface-related effects on the spatial variation in the structural and orientational ordering, hydrogen bond (H-bond) organization, and local density of H2O molecules at this important model phyllosilicate surface. MD simulations at constant temperature and volume (statistical NVT ensemble) were performed for a series of model systems consisting of a two-layer muscovite slab (representing 8 crystallographic surface unit cells of the substrate) and 0 to 319 adsorbed H2O molecules, probing the atomistic structure and dynamics of surface aqueous films up to 3 nm in thickness. The results do not demonstrate a completely liquid-like behavior, as otherwise suggested from the interpretation of X-ray reflectivity measurements and earlier Monte Carlo simulations. Instead, a more structurally and orientationally restricted behavior of surface H2O molecules is observed, and this structural ordering extends to larger distances from the surface than previously expected. Even at the largest surface water coverage studied, over 20% of H2O molecules are associated with specific adsorption sites, and another 50% maintain strongly preferred orientations relative to the surface. This partially ordered structure is also different from the well-ordered 2-dimensional ice-like structure predicted by ab initio MD simulations for a system with a complete monolayer water coverage. However, consistent with these ab initio results, our simulations do predict that a full molecular monolayer surface water coverage represents a relatively stable surface structure in terms of the lowest diffusional mobility of H2O molecules along the surface. Calculated energies of water adsorption are in good agreement with available experimental data.