  The recent data collected by {\it Herschel} have confirmed that interstellar
structures with filamentary shape are ubiquitously present in the Milky Way.
Filaments are thought to be formed by several physical mechanisms acting from
the large Galactic scales down to the sub-pc fractions of molecular clouds, and
they might represent a possible link between star formation and the large-scale
structure of the Galaxy. In order to study this potential link, a statistically
significant sample of filaments spread throughout the Galaxy is required. In
this work we present the first catalogue of $32,059$ candidate filaments
automatically identified in the Hi-GAL survey of the entire Galactic Plane. For
these objects we determined morphological (length, $l^{a}$, and geometrical
shape) and physical (average column density, $N_{\rm H_{2}}$, and average
temperature, $T$) properties. We identified filaments with a wide range of
properties: 2$'$\,$\leq l^{a}\leq$\, 100$'$, $10^{20} \leq N_{\rm H_{2}} \leq
10^{23}$\,cm$^{-2}$ and $10 \leq T\leq$ 35\,K. We discuss their association
with the Hi-GAL compact sources, finding that the most tenuous (and stable)
structures do not host any major condensation and we also assign a distance to
$\sim 18,400$ filaments for which we determine mass, physical size, stability
conditions and Galactic distribution. When compared to the spiral arms
structure, we find no significant difference between the physical properties of
on-arm and inter-arm filaments. We compared our sample with previous studies,
finding that our Hi-GAL filament catalogue represents a significant extension
in terms of Galactic coverage and sensitivity. This catalogue represents an
unique and important tool for future studies devoted to understanding the
filament life-cycle.
