The European Space Agency Euclid mission is a space telescope that aims to understand dark matter and dark energy.
Dark energy causes the expansion of the Universe to accelerate over time.
On the other hand, dark matter is like ordinary matter, but it does not absorb or emit light, and so its existence can only be inferred by the gravitational pull.
Explaining what dark matter and dark energy are, and how they fit into the standard model of physics, poses a great challenge for cosmologists.
The Euclid telescope will measure the effects of both dark matter and dark energy by looking over great distances and mapping the distribution of galaxies over 10 billion years of cosmic time. The mission is the result of a consortium of 17 countries. Euclid launch on 2023, 1 July successful, now on its way to L2.

For more info: Euclid Consortium - Euclid - ESA

Artist views of the Euclid Satellite - Credits: ESA

Euclid will measure two different cosmological phenomena.
First, it will map the three-dimensional distribution of galaxies, the so-called cosmic web. The telescope has two cameras, one sensitive to visible light and one to near infrared light, as well as a spectrograph for making redshift measurements.

By carrying out statistical analyses on the resulting galaxy maps, cosmologists can measure the baryon acoustic oscillations, the remnant signal from pressure waves in the hot plasma in the early Universe.
This signal encodes a reference distance that can be tracked over time to measure the expansion of the Universe and test dark energy models.

Euclid will measure the expansion of the Universe to understand the effects of dark energy and dark matter. (credit ESA, https://sci.esa.int/web/euclid/-/46673-expansion-history-of-the-universe).

Second, Euclid will measure the shapes of galaxies extremely precisely to detect the slight distortions that are caused by gravitational lensing.
As light travels to us from distant galaxies, it bends under the pull of gravity, like light passing through a glass lens.
The amount of distortion tells us about the abundance of matter along the line of sight. The maps constructed based on gravitational lensing allow us to measure the matter distribution, even if it cannot be seen directly, as in the case for dark matter.

Euclid will measure the distortions of galaxy shapes due to gravitational lensing to make maps of the dark matter. (credit NASA, ESA and L. Calçada, https://esahubble.org/images/heic1106c/).

Euclid will observe 15,000 deg² of extragalactic sky and measure 1.5 billion galaxies with high resolution imaging.
The rich data set will allow astronomers to study galaxies, both in the near and distant Universe, to understand how galaxies form and evolve over time.
It will also tell us about the environment inside galaxy clusters which are the most massive structures in the Universe.
Closer to home, Euclid will measure the stars in the bulge of our own Milky Way Galaxy and help to understand how it formed.

A simulated view of the Universe from Euclid. (credit Euclid Consortium, https://sci.esa.int/web/euclid/-/61404-predicted-view-of-the-euclid-deep-field-fornax).

Within the Euclid Science Ground Segment (SGS), we lead the RICH-CL Processing Function in charge of determining the richness of clusters of galaxies observed by Euclid and the membership probability of their galaxies.
We also co-lead two programs, parts of the key project "Characterization of the properties of detected galaxy clusters" dealing with the mentioned richness and membership assignment for Euclid-detected clusters and with the full Richness-mass calibration of Euclid-detected clusters.
Within the Rubin-Euclid Derived Data Products Working Group, we recommended a number of joint data products to enhance the science yield by matching depths across observatories and facilitating galaxy and cluster detection.

Link: archive OAB web page for Euclid mission (in italian).