  ESPRESSO is the new high-resolution spectrograph of ESO's Very-Large
Telescope (VLT). It was designed for ultra-high radial-velocity precision and
extreme spectral fidelity with the aim of performing exoplanet research and
fundamental astrophysical experiments with unprecedented precision and
accuracy. It is able to observe with any of the four Unit Telescopes (UT) of
the VLT at a spectral resolving power of 140,000 or 190,000 over the 378.2 to
788.7 nm wavelength range, or with all UTs together, turning the VLT into a
16-m diameter equivalent telescope in terms of collecting area, while still
providing a resolving power of 70,000. We provide a general description of the
ESPRESSO instrument, report on the actual on-sky performance, and present our
Guaranteed-Time Observation (GTO) program with its first results. ESPRESSO was
installed on the Paranal Observatory in fall 2017. Commissioning (on-sky
testing) was conducted between December 2017 and September 2018. The instrument
saw its official start of operations on October 1st, 2018, but improvements to
the instrument and re-commissioning runs were conducted until July 2019. The
measured overall optical throughput of ESPRESSO at 550 nm and a seeing of 0.65
arcsec exceeds the 10% mark under nominal astro-climatic conditions. We
demonstrate a radial-velocity precision of better than 25 cm/s during one night
and 50 cm/s over several months. These values being limited by photon noise and
stellar jitter show that the performanceis compatible with an instrumental
precision of 10 cm/s. No difference has been measured across the UTs neither in
throughput nor RV precision. The combination of the large collecting telescope
area with the efficiency and the exquisite spectral fidelity of ESPRESSO opens
a new parameter space in RV measurements, the study of planetary atmospheres,
fundamental constants, stellar characterisation and many other fields.
