Non-Gaussianity and merger rate of primordial black holes

Primordial Black Holes (PBHs) might constitute a non negligible fraction of the dark matter and allow us to study the early Universe at scales inaccessible by Cosmic Microwave Background anisotropies and other observables. The interest in their study has grown in recent years since the first LIGO gravitational waves detection. PBHs could have formed from the collapse of primordial perturbations generated during inflation. For example in this Thesis we review their production in the so called ``ultra slow-roll'' and ``inflation fall'' scenarios. Their formation depends on the shape of the primordial power spectrum, and the existence of primordial non-Gaussianity (NG) can play a crucial role in PBH generation and abundance. We analyzed how the scenario is modified in the presence of primordial NG, and how this can be used to set constraints on PBHs. We develop a formalism to include the effects of non-Gaussianity, initial clustering and binary formation in the calculation of PBH merger rate. This newly developed formalism can be used to explore different scenarios for PBH abundance and mass functions.