This introduction presents an overview of key concepts discussed in the subsequent chapters of this book. The book is about abstract entities. It provides an opinionated introduction to the metaphysics of abstract entities. The book focuses on the main arguments that structure the contemporary debate over their nature and existence. The primary concern of the book is with the fate of austere versions of Platonism, which uphold substantive generalizations about abstract entities—:e.g., that they are causally inactive or without spatiotemporal location—and eschew the abstract entities posited by expansive Platonists. The book also explains the nature and appeal of Platonism as a metaphysical thesis. It also surveys regress arguments as well as appeals to parsimony and paradox sometimes offered in defence of nominalism. The book also focuses on the non-uniqueness problem, which generates worries about arbitrariness and under determination for certain versions of Platonism.