  We present a detailed study of the hydrogen density distribution in the local
interstellar medium (ISM) using the X-ray absorption technique. Hydrogen column
densities were precisely measured by fitting X-ray spectra from coronal sources
observed during the initial {\it eROSITA} all-sky survey (eRASS1). Accurate
distance measurements were obtained through cross-matching Galactic sources
with the {\it Gaia} third data release (DR3). Despite the absence of a
discernible correlation between column densities and distances or Galactic
longitude, a robust correlation with Galactic latitude was identified. This
suggests a decrease in ISM material density along the vertical direction away
from the Galactic plane. To further investigate, we employed multiple density
laws to fit the measured column densities, revealing constraints on height
scale values ($8 < h_{z} < 30$~pc). Unfortunately, radial scales and central
density remain unconstrained due to the scarcity of sources near the Galactic
center. Subsequently, a 3D density map of the ISM was computed using a Gaussian
processing approach, inferring hydrogen density distribution from hydrogen
column densities. The results unveiled the presence of multiple beams and
clouds of various sizes, indicative of small-scale structures. Large density
regions were identified at approximately 100~pc, consistent with findings in
dust reddening studies, potentially associated with the Galactic Perseus arm.
Moreover, high-density regions were pinpointed in proximity to the Orion
star-forming region and the Chamaeleon molecular complex, enriching our
understanding of the intricate structure of the local interstellar medium.
