The first part of this chapter is concerned with the process of analytic continuation abstracting from particular methods. It culminates in a proof of the monodromy theorem with various applications to proper mappings and algebraic functions. The second part is devoted to the generalisation of the Riemann mapping theorem to arbitrary domains, known as the uniformisation theorem. Two proofs of this fundamental theorem and of important corollaries like the invariant Schwarz lemma and the subordination principle are presented.