This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book is concerned with the second problem, to which it will present a solution. It assumes as correct most of the epochmaking contributions Karl Popper has made to the first problem, that of knowledge and its growth, which has been one of his principal philosophical interests. The book explains briefly why it is important to refute these positions by solving the problem, and shall outline strategy for dealing with it. It proceeds to consider the historical background behind the construction of theories of rationality, and discusses critically two influential but unsuccessful specimen theories of rationality. The book presents an alternative theory of rationality which, freed of these dogmas, is able successfully to solve the problem of rationality and its limits. Philosophical incapacity to answer the fideistic and skeptical claim and argument has some serious consequences.