Primordial Black Holes (PBHs) may be produced by gravitational collapse in regions with a large amplitude of density contrasts in the early Universe. They may provide the seeds for galaxy formation, account for a population of the LIGO-Virgo events, and the candidates of cold dark matter. Measurements or constraints on their abundance can be regarded as a probe of the inflationary models. In this seminar, I will show this by studying an inflation model that glues two linear potentials of different slopes, which is a simple toy model to enhance the inflationary scalar perturbations at small scales naturally. The enhanced perturbation can produce PBHs, together with gravitational waves induced through higher-order gravitational interactions between enhanced scalar and tensor fluctuations. Moreover, a very important issue about PBH is how to accurately estimate its abundance, as it is the observable quantity that can be detected directly. Apart from the Press Schechter method and the Compaction function method, people are developing a more precise method with using of the peak's theory. In the latter half of this seminar, I will talk about how to use the peak's theory to estimate the PBH abundance, especially for perturbations with a finite-width.