Analytic continuation is the extension of the domain of a given analytic function in the complex plane, to a larger domain of the complex plane. This process has been utilized in many other areas of mathematics, and has given mathematicians new insight into some of the world???s hardest problems. This paper will cover more general forms of analytic continuation, which will be referred to as generalized analytic continuations. The paper will closely follow William Ross??? and Harold Shapiro???s book ???Generalized Analytic Continuation??? , with the proofs worked out with more detail, and a few generalizations are made regarding the Poincare example in Section 3.3.