The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a an array of topics in classical analysis, as described in this book. The authors use the strong analogy with the summability of divergent series to motivate the subject. In this vein, for instance, theorems can be described as being Abelian or Tauberian. The introductory overview carefully explains the history and context of the theory.