A method to explore the column density of the Local Interstellar Medium (LISM) using absorptions in the resonance H and K lines of Mg II. The intrinsic strengths of these lines in the temperature and density conditions prevailing in warm clouds in the LISM allows them to be used to explore many lines of sight where lines such a NaD and Ca II H and K are too weak, but where L-alpha is saturated. The number of measurable lines-of-sight is greatly enhanced by using cool stars as the background emitters, but this implies reliable separation of the LISM components from stellar chromospheric self-absorptions. A combination of column density and radial velocity data is used to measure the spatial extent and the physical parameters of the single cloud in which the sun is embedded. This proves to be an oblate spheroid.