Dwarf galaxies are expected to play a key role in galaxy formation and evolution. In hierarchical models they are thought to be the first structures to form in the Universe and are believed to have an important contribution to the reionisation process. Investigating the detailed properties of dwarf galaxies around the peak of cosmic star formation history (z ~ 2) is therefore an important test of structure formation in ΛCDM. Spatially resolved studies of the star formation activity and the metal enrichment provide powerful diagnostic tools: metallicity gradients are thought to be highly sensitive to the gas surface density, its kinematic structure (coherent rotation vs unordered motions), and the prevalence of inflows and outflows. Distant sub-M* galaxies have faint apparent magnitudes and we still have limited knowledge of their morphological and chemodynamical properties (e.g., Kassin et al. 2012; van der Wel et al. 2014; Kartaltepe et al. 2015; Whitaker et al. 2015; Simons et al. 2015). The samples for which spatially-resolved kinematics can be obtained remain small and the integration times very large (e.g., Contini et al. 2016).

Simulations show that mapping the properties of the ionised haloes of starbursting dwarfs similar to Haro11 at z ~ 2 should be feasible in ~10hr with multi-IFU observations. Typical logM* = 9 galaxies at z = 2 have internal velocity dispersions ???? < 50 km/s (Mason et al. 2016), which MOSAIC will be able to resolve but JWST/NIRSpec will struggle with. In addition to enabling the measurement of (spatially-resolved) internal motions, resolving emission lines down to ???? ~ 10 km/s will be critical to unveiling the presence of the narrow kinematical subcomponents that are characteristic of rapidly assembling dwarfs (Amorin et al. 2012)--and which indicate that star formation typically proceeds in an ensemble of several compact and turbulent clumps.

	The oldest and lowest metallicity stars that exist today carry the imprint of the first massive stars that ended their lives as supernovae. We can constrain star formation in very metal-poor environments by analysing the metallicity distribution functions (MDFs) of stellar populations in the local Universe. Specifically, we are interested in probing the MDFs in a variety of environments, from the outer stellar halo in the Galaxy to the bulge, as well as in other galaxies in the Local Group (mostly dwarf spheroidals and ultra-diffuse dwarfs).

The characterization of primordial stars in the Galaxy has great scientific potential. These stars are the long-lived descendants from the earliest stellar generations and will have formed from a (near-)pristine ISM, which would have only been weakly enriched in metals from the first supernovae. Their atmospheres therefore give us a fossil record of the ISM from which they were formed, corresponding to redshifts of z ≥ 10. Having a direct tracer of chemical abundances at such an early time can provide fundamental constraints on the properties of the first generations of stars. The limit of the current observations do not allow to discriminate between different theoretical models on e.g. the need and the level of a “critical metallicity” for the formation of low mass stars. MOSAIC will allow to greatly increase the constraints on the low-metallicity tail of the MDF which would result in stronger constraints on the formation models.

The stellar populations of the Galactic bulge are a template for studies of ellipticals and bulges of spirals. The formation history of the bulge can give hints on proto-galaxy counterparts observed at high-redshift, providing strong motivation for the detailed study of this component of our Galaxy. The formation of our bulge is still a controversial issue, and it is probably a combination of a pseudo-bulge population, and an old, spheroidal, true bulge. Studies of the chemical compositions and kinematics of its stellar populations will be the key to disentangle its formation mechanism(s). Current high-spectral resolution observations in the optical (e.g. with VLT/FLAMES) are limited to giant stars, but observations of dwarfs will be important to disentangle the complex mix of stellar populations in the bulge. Currently, few dwarfs have been studied via microlensing techniques, but with MOSAIC a significantly larger population of dwarf will be accessible in the Galactic bulge.

As for extragalactic studies, the current limiting factor is that only giant stars are bright enough to have high quality, high-resolution spectroscopy with an 8-m class telescope. Unfortunately, the statistics available from the analysis of extragalactic red giant branch (RGB) stars is not sufficient to determine the metal-poor tail of the MDF robustly in their host galaxies. There are simply not enough giant-branch stars in most of the LG dwarf galaxies to sample these rare populations and to observe these faint stars in extragalactic systems we need the sensitivity of the E-ELT. One then needs large samples of stars at the main-sequence turn-off (MSTO), in multiple nearby galaxies.

The identification of the main ionizing sources has been elusive until know due to their faintness. Thanks to its larger collecting area, the ELT will allow us to push the search of these sources to much fainter magnitudes and higher redshifts, compared to the currently achieved with 8-10 m telescopes. The overarching goal is to derive a precise characterization of the ionisation state of the IGM during the first Gyr of the life of the Universe, to construct the timeline and topology of reionisation, and to observe the formation and growth of the first galaxies.

Very deep optical-to-near-IR spectroscopy to probe the UV rest-frame emission of galaxies in the early Universe is crucial to study these questions. Some of the fundamental questions and hot topics are:

• Measurements of Ly-alpha emission in galaxies (i.e., fraction of Ly-alpha emitters in the Lyman break galaxy population, evolution of the Ly-alpha luminosity function with redshift, Ly-alpha equivalent width measurements and information from the detailed Ly-alpha line profile, see Dijkstra et al. 2013, Mesinger et al. 2015, Mason et al. 2018) provide crucial information on the ionization state of the IGM;
• Overdensities of Ly-alpha emitters at z~7-8 (Castellano et al. 2016, Tilvi et al. 2020) providing the first evidence for overlapping reionized bubbles in the IGM, i.e. a hint of topology. Also, the detailed Ly-alpha line profile of z>>6 galaxies can constrain the properties of reionized bubbles in the early Universe (Haiman 2002, Mason & Gronke 2020);
• One of key quantities to establish if galaxies reionized the Universe, is the measurement of escape fraction of Lyman continuum photons, fesc, which relies on measurements of the Ly-alpha line profile (121.6 nm), the MgII doublet line (280.7,280.9 nm), and UV low ionization absorption lines (e.g. SiII 126.0 nm) (Izotov et al. 2018, Verhamme et al. 2017, Reddy et al. 2018, Gazagnes et al. 2018, Chisholm et al. 2018, 2020). In contrast, no reliable method has yet been found to determine fesc from rest-frame optical spectra (see e.g. Plat et al. 2019, Wang et al. 2020);
• UV absorption lines and nebular emission lines also provide fundamental information on the ISM of high-z galaxies, such as the geometry and properties of the gas (outflows, the presence of channels allowing LyC photon escape, gas density, and others), chemical abundances (C, O, and Si, e.g);
• Spectroscopy of distant galaxies with 8-10m class telescopes reveal UV emission lines that require moderately metal-poor gas and a harder radiation field than is seen in galaxies at lower redshift (cf. review by Stark 2016). Several z>6 galaxies show the presence of CIV 154.8nm emission, others HeII 164 nm, [OIII] 166.7 nm, [CIII] 190.9 nm with varying intensities. However, both nebular CIV and HeII emission, requiring higher energies, is challenging to produce and their origin is intensely debated (e.g. Schaerer et al. 2018, Saxena et al. 2019). Spatially resolved studies in, e.g., HeII in emission will be essential to constrain the ionizing sources;
• Structure formation can also be investigated at the epoch of reionisation by looking for proto-clusters (Toshikowa et al. 2014; Overzier et al. 2016). Spatially-resolving the galaxies and AGN, and studying the circum-galactic and inter-galactic medium (CGM and IGM) within these proto-clusters provides us a unique opportunity to witness the early formation, growth, and co-evolution of these structures on a huge range of spatial scales.