Our current understanding of the subatomic world is based on the Standard Model of elementary particle physics, a description of all known subatomic particles and forces in the language of quantum field theory (QFT). The theoretical basis of the Standard Model was laid in the 1960s, while its successive experimental confirmation since then has been a continuous success story that culminated in the discovery of the Higgs boson at CERN in 2012. While the Standard Model represents an unmatched triumph of fundamental physics, several observations provide us with clear evidence that it must be incomplete. The Standard Model fails to incorporate Einstein's theory of gravity at the quantum level; it treats neutrinos as massless particles, even though the observation of neutrino oscillations points to nonzero neutrino masses; and it cannot explain dark matter and dark energy; just to name a few mysteries that the Standard Model is unable to address. We have therefore now entered the era of physics beyond the Standard Model (BSM), a new age in particle physics devoted to the search for "new physics". A prime role in this quest is played by axions, an exciting class of hypothetical subatomic particles that promise attractive solutions to many of the shortcomings of the Standard Model. Originally theorized in the context of quantum chromodynamics (QCD),the theory of the strong nuclear force, axions can explain puzzling properties of QCD, represent a promising candidate for dark matter, and might be responsible for dark energy. AxiBAU especially focused on axion physics in the context of early-Universe cosmology. Cosmological axion models can explain processes such as cosmic inflation, the stage of exponential expansion in the very early Universe; predict a wealth of exciting observational signatures, e.g. in terms of primordial magnetic fields, black holes, and gravitational waves; and hence serve as an excellent benchmark for theoretical studies and future observations. Moreover, it has been realized in recent years that axions may play a major role in the generation of the baryon asymmetry of the Universe. That is, they may explain the puzzling observation that our Universe seems to consist almost exclusively of matter instead of antimatter, even though our QFT description of the early Universe has no clear preference for one over the other. The matter-antimatter asymmetry is a well-measured quantity in cosmology. Any cosmological axion model resulting in "baryogenesis" is therefore constrained by the fact that it must not lead to too large an asymmetry. In order to develop a robust understanding of cosmological axion models and arrive at reliable predictions for future observations, it is therefore mandatory to have exquisite theoretical control over the process of axion-driven baryogenesis (ADB) in the early Universe, which precisely defines AxiBAU's primary objective. The overall aim of the project was to improve the technical description of existing ADB models, unify and connect existing models, as well as to construct and study new models. In this sense, AxiBAU epitomized the spirit of BSM physics in the 21st century, which no longer relies exclusively on collider searches for new physics but which combines particle physics, astroparticle physics, and cosmology in a new interdisciplinary effort. AxiBAU was concerned with questions in fundamental science and thus did not yield any commercial applications. Instead, it explored ideas that are essential to our worldview and relevant to all members of society who ponder our place in the cosmos. With a bit of luck, the contemporary research on axion cosmology will one day lead to the next discovery of a new elementary particle: after the discovery of the Higgs boson at CERN almost ten years ago, the next step might be the discovery of an axion in the sky.
