  For the vast majority of stars in the second Gaia data release, reliable
distances cannot be obtained by inverting the parallax. A correct inference
procedure must instead be used to account for the nonlinearity of the
transformation and the asymmetry of the resulting probability distribution.
Here we infer distances to essentially all 1.33 billion stars with parallaxes
published in the second \gaia\ data release. This is done using a weak distance
prior that varies smoothly as a function of Galactic longitude and latitude
according to a Galaxy model. The irreducible uncertainty in the distance
estimate is characterized by the lower and upper bounds of an asymmetric
confidence interval. Although more precise distances can be estimated for a
subset of the stars using additional data (such as photometry), our goal is to
provide purely geometric distance estimates, independent of assumptions about
the physical properties of, or interstellar extinction towards, individual
stars. We analyse the characteristics of the catalogue and validate it using
clusters. The catalogue can be queried on the Gaia archive using ADQL at
http://gea.esac.esa.int/archive/ and downloaded from
http://www.mpia.de/~calj/gdr2_distances.html .
