  High synchrotron peaked blazars (HSPs or HBLs) play a central role in very
high energy (VHE) gamma-ray astronomy, and likely in neutrino astronomy.
Currently, the largest compilation of HSP blazars, the 2WHSP sample, includes
1691 sources, but it is not complete neither in the radio nor in the X-ray
band. In order to provide a more sizable and more accurate set of HSP blazars
that is useful for future statistical studies and to plan for VHE/TeV
observations, we present the largest sample of extreme and high synchrotron
peaked (EHSP;HSP) blazars and blazar candidates: the 3HSP catalogue. The 3HSP
catalogue includes 2013 sources, 88% of which with a redshift estimation, a
much larger percentage than in any other list of HSP blazars. All new
{\gamma}-ray detections are described in the First and Second Brazil ICRANet
gamma-ray blazar catalogues (1BIGB & 2BIGB) also taking into account the 4FGL
list of {\gamma}-ray sources published by the Fermi large area telescope
(Fermi-LAT) team. Moreover, the cross-matching between the 2WHSP, 2FHL HSPs,
and IceCube neutrinos position has suggested that HSPs are likely counterparts
of neutrino events, which implies the 3HSP catalogue is useful also in that
respect. The 3HSP catalogue features improved completeness compared to its
predecessors, the 1WHSP and 2WHSP catalogues, and follows the track of their
increasing relevance for VHE astronomy.
