The gamma-ray blazar TXS 0506+056, was discovered in VHE gamma-rays
by the MAGIC telescopes in 2017 in a follow-up campaign of a high energy neutrino
event IceCube-170922A (IC+Fermi+MAGIC++, Science 361, eaat1378 (2018)). Subsequent
multivawelenght (MWL) observations
and theoretical modeling in a frame of hadro-leptonic emission confirmed that this
source could be a potential cosmic ray and neutrino emitter
(MAGIC Collaboration, Ansoldi et al., (2018)).
This is, by far, the most significant association between a high-energy neutrino
and an astrophysical source emitting gamma rays and X-rays. TXS 0506+056 is a key object
to help the astrophysics community to establish connections between high-energy neutrinos
and astrophysical sources. Accurate and contemporaneous MWL spectral measurements are essential ingredients to achieve this goal.
In the conference, we present the measurements
from the MAGIC and MWL monitoring of this source, spanning the time period
from November 2017 till February 2019. These include the lowest VHE gamma-ray emission state measured from this source so far as well as a flaring episode in December 2018.