Primordial Black Holes from Inflation

The study of Primordial Black Holes (PBHs) allows us to gain a deep insight into the early Universe since it gives access to much smaller scales than the CMB scales and it could potentially put strict limits on inflationary models. This thesis aims to put an upper limit on the amplitude of the power spectrum associated to the formation of a PBH by means of recent observational constraints on the PBHs abundance. We use the results of recent numerical simulations in the framework of the general relativistic collapse and peaks theory to connect the formation of PBHs in real space to a generic feature in the primordial curvature power spectrum. Moreover, we investigate the effects that the choice of a particular window function has on the power spectrum.