  The occurrence of multiple stars, dominantly binaries, is studied using the
\textit{Gaia}-ESA DR2 catalogue. We apply the optimized statistical method that
we previously developed for the analysis of 2D patterns. The field of stars is
divided into a mosaic of small pieces, which represent a statistical set for
analysis. Specifically, data input is represented by a grid of circles (events)
with radius $0.02\,\deg$ covering the sky in the field of galactic latitude
$\left\vert b\right\vert >25\,\deg$. The criteria for selecting candidates for
multiple stars are based on two parameters: angular separation and collinearity
of proper motion. Radial separation, due to limited accuracy, is used only as a
weaker supplementary constraint. Due attention is paid to the accurate
calculation of the background, which is a necessary input for evaluating the
quality of the candidates. Our selection algorithm generates the catalogue of
candidates: $900,842$ binaries, $5,282$ trinaries and $30$ quaternaries.
