The conference was held at the Vatican Observatory in Castel Gandolfo, from 17 to 20 June 2024. The dates fell fifty-seven years after Lemaître's death, and on the eve of the centenary of his foundational 1927 paper on the expanding universe.

The collection gathers nineteen contributions, plus an editorial article. Together they address the most pressing open problems at the interface of cosmology, gravitation and quantum theory. Topics range from the Hubble tension to the future of ΛCDM in light of recent DESI data. They include inflationary cosmology and dark-energy model-building in string theory and supergravity, together with the Swampland constraints that bound them. They address the observer-dependence of the quantum-cosmological wave function. They cover the removal, or consistent crossing, of spacetime singularities, from the canonical quantization of Lemaître's own 1933 dust model to string-theoretic pre-Big-Bang bounces and many-body constructions of singularity-free black-hole cores. They also address primordial black holes and their gravitational-wave signatures. Further contributions search for a background-independent formulation of quantum gravity and a first-principles account of horizon thermodynamics. Others examine the foundational status of the quantum-to-classical transition in gravitational contexts. A proposal for lunar-based cosmological observations completes the collection, together with a historical reconstruction of the genesis of Lemaître's primeval-atom hypothesis.

A recurring unifying thread has been the legacy of Lemaître himself. He was the first scientist to understand the importance of the cosmological constant in the Einstein equations and the instability of static universe models, in General Relativity, proposed by Einstein himself. He proposed an initial quantum mechanical phase of our universe that he called “Primeval Atom”. This was the first attempt to join Quantum Mechanics with General Relativity, a theory now known as Quantum Gravity. In Black-Hole solutions, he was the first one too to distinguish coordinate from physical singularities (Eddington–Finkelstein coordinates). He also coined the term "horizon” for a Black Hole. His pioneering vision continues to guide research at the frontier of cosmology and fundamental physics.