The main purpose of this book section is to briefly summarize the types of generating functions and some of their properties. Another purpose is to give some specific families of generating functions with their applications and examples, combined with new and known results. In particular, in order to highlight the generating functions that I have discovered in recent years, some of their fundamental properties are given. Perhaps most importantly, to provide open questions that are relevant to the subject and will open new horizons for interested researchers. Moreover, another important purpose of this section is to provide solved examples and to adorn with numerous exercises, depending on the extension of interested researchers to create research areas.