The standard Λ Cold Dark Matter cosmological model provides an amazing description of a wide range of astrophysical and astronomical data. However, there are a few big open questions, that make the standard model look like a first-order approximation to a more realistic scenario that still needs to be fully understood. In this Letter of Interest we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances present between the different cosmological probes, as the Hubble constant H0 value, the σ8S8 tension, and the anomalies present in the Planck results. Finally, we will give an overview of upgraded experiments and next-generation space-missions and facilities on Earth that will be of crucial importance to address all these questions.What is the nature of dark energy and dark matter? Did the universe have an inflationary period? How did it happen? What is the level of non-gaussianities? Does gravity behave like General Relativity even at horizon size scales? Is there Modified Gravity? Do we need quantum gravity, or an unified theory for quantum field theory and General Relativity? Is the universe flat, open or closed? What is the age of the universe? Do we actually need physics beyond the Standard Model (SM) of particle physics? For each elementary particle, there is an antiparticle that has exactly the very same properties but opposite charge. Then, why we do not see antimatter in the universe? Will the swampland conjectures of string theory help with fine-tuning problems in cosmology? Alternatively, will cosmology help us observationally test conjectures from string theory?