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Reasoning in Simple Type Theory is a collection of papers that includes reprints of eight seminal papers in this area as well as thirteen new contributed articles. For the reprints we have chosen a paper by Alonzo Church (introducing his simple theory of types), a paper by Leon Henkin (proving completeness of Church's type theory relative to Henkin's semantics) and some of the most important papers by Peter Andrews. The new articles were contributed by Peter Andrews and his students and collaborators as well as a number of researchers his work has influenced. The volume intends to show the historical development of this important area of formal reasoning up to its current state of art and appears in honor of Peter Andrews on his 70th birthday.