Title: Algebraic Patching for Beginners
Abstract: Using the language and the tools of rigid analytic geometry, Harbater (1987) has defined a "patching operation" which can be used to solve the inverse Galois problem over fields like Qₚ(T) or Fₚ((X))(T). Later, Haran and Völklein (1996) rephrased this construction in a purely algebraic language, replacing all geometric arguments with (almost entirely) explicit constructions. Our goal is to present their proof.