In recent years, millisecond duration radio signals originating from distantgalaxies appear to have been discovered in the so-called Fast Radio Bursts.These signals are dispersed according to a precise physical law and thisdispersion is a key observable quantity which, in tandem with a redshiftmeasurement, can be used for fundamental physical investigations. While everyfast radio burst has a dispersion measurement, none before now have had aredshift measurement, due to the difficulty in pinpointing their celestialcoordinates. Here we present the discovery of a fast radio burst and theidentification of a fading radio transient lasting $\sim 6$ days after theevent, which we use to identify the host galaxy; we measure the galaxy'sredshift to be $z=0.492\pm0.008$. The dispersion measure and redshift, incombination, provide a direct measurement of the cosmic density of ionisedbaryons in the intergalactic medium of $\Omega_{\mathrm{IGM}}=4.9 \pm 1.3\%$,in agreement with the expectation from WMAP, and including all of the so-called"missing baryons". The $\sim6$-day transient is largely consistent with a shortgamma-ray burst radio afterglow, and its existence and timescale do not supportprogenitor models such as giant pulses from pulsars, and supernovae. Thiscontrasts with the interpretation of another recently discovered fast radioburst, suggesting there are at least two classes of bursts.

We investigate data from the Galactic Effelsberg--Bonn HI Survey (EBHIS),supplemented with data from the third release of the Galactic All Sky Survey(GASS III) observed at Parkes. We explore the all sky distribution of the localGalactic HI gas with $|v_{\rm LSR}| < 25 $ kms$^{-1}$ on angular scales of 11'to 16'. Unsharp masking (USM) is applied to extract small scale features. Wefind cold filaments that are aligned with polarized dust emission and concludethat the cold neutral medium (CNM) is mostly organized in sheets that are,because of projection effects, observed as filaments. These filaments areassociated with dust ridges, aligned with the magnetic field measured on thestructures by Planck at 353 GHz. The CNM above latitudes $|b|>20^\circ$ isdescribed by a log-normal distribution, with a median Doppler temperature$T_{\rm D} = 223$ K, derived from observed line widths that include turbulentcontributions. The median neutral hydrogen (HI) column density is $N_{\rm HI}\simeq 10^{19.1}\,{\rm cm^{-2}}$. These CNM structures are embedded within awarm neutral medium (WNM) with $N_{\rm HI} \simeq 10^{20} {\rm cm^{-2}}$.Assuming an average distance of 100 pc, we derive for the CNM sheets athickness of $< 0.3$ pc. Adopting a magnetic field strength of $B_{\rm tot} =(6.0 \pm 1.8)\mu$G, proposed by Heiles & Troland 2005, and assuming that theCNM filaments are confined by magnetic pressure, we estimate a thickness of0.09 pc. Correspondingly the median volume density is in the range $ 14 < n <47 {\rm cm^{-3}}$.