Textbook in PDF format Primordial black holes (PBHs) were proposed more than 50 years ago as black holes possibly formed across a vast mass range in the early universe. They represent a unique probe to access the primordial universe and cosmological inflation. Furthermore, in certain mass ranges, they could comprise the entirety of the dark matter, seed supermassive black holes at high redshift, be responsible for some gravitational-wave events detected so far, and be novel gravitational-wave sources detectable with future instruments. However, detecting PBHs has proved to be extremely challenging and extensive research focused on setting a variety of constraints on the fraction of dark matter composed by these objects