Teoria Gravitazionale e Applicazioni Cosmologiche: Possibili Sviluppi Futuri

A very short, non-technical review of the main problems which are presently open in the context of the gravitational theory and of its cosmological applications, and which are currently under investigation and deep discussion. We will talk in particular about the equivalence principle, the dark matter and dark energy contributions, the cosmological constant, the quantisation of gravity, the dynamics of the very early Universe.