  In this article we discuss the importance of high-resolution absorption
spectroscopy for our understanding of the distribution and physical nature of
the gaseous circumgalactic medium (CGM) that surrounds the Milky Way.
Observational and theoretical studies indicate a high complexity of the gas
kinematics and an extreme multi-phase nature of the CGM in low-redshift
galaxies. High-precision absorption-line measurements of the Milky Way's gas
environment thus are essential to explore fundamental parameters of
circumgalactic gas in the local Universe, such as mass, chemical composition,
and spatial distribution. We shortly review important characteristics of the
Milky Way's CGM and discuss recent results from our multi-wavelength
observations of the Magellanic Stream. Finally, we discuss the potential of
studying the warm-hot phase of the Milky Way's CGM by searching for extremely
weak [FeX] l6374.5 and [FeIVX] l5302.9 absorption in optical QSO spectra.
