  We present a detailed study of X-ray absorption in the local interstellar
medium by analyzing the X-ray spectra of 24 galactic sources obtained with the
{\it Chandra} High Energy Transmission Grating Spectrometer and the {\it
XMM-Newton} Reflection Grating Spectrometer. By modeling the continuum with a
simple broken power-law and by implementing the new {\tt ISMabs} X-ray
absorption model, we have estimated the total H, O, Ne, and Fe column densities
towards the observed sources. We have determined the absorbing material
distribution as a function of source distance and galactic latitude--longitude.
Direct estimates of the fractions of neutrally, singly, and doubly ionized
species of O, Ne, and Fe reveal the dominance of the cold component, thus
indicating an overall low degree of ionization. Our results are expected to be
sensitive to the model used to describe the continuum in all sources.
