  ESPRESSO is a new high-resolution ultra-stable spectrograph for the VLT,
which had its first light on Telescope on November 27th, 2017. The instrument
is installed in the Combined Coud\'{e} Laboratory and linked to the 4 Units of
Telescope through optical Coud\'{e} Trains, being the first spectrograph able
to collect the light from the 4 UTs simultaneously. One of the key science
goals of the instrument is to test the stability of nature's fundamental
couplings with unprecedented resolution and stability. ESPRESSO will allow to
eliminate current known systematics and test the claim by Webb et al 2012 of a
spatial dipole in the variation of the fine-structure constant. These improved
results (either null or variation detections) will put strong constraints on a
range of cosmological and particle physics parameters.
