Reasoning in Simple Type Theory is a collection of papers thatincludes reprints of eight seminal papers in this area as well asthirteen new contributed articles. For the reprints we have chosen apaper by Alonzo Church (introducing his simple theory of types), apaper by Leon Henkin (proving completeness of Church's type theoryrelative to Henkin's semantics) and some of the most important papersby Peter Andrews. The new articles were contributed by Peter Andrewsand his students and collaborators as well as a number of researchershis work has influenced. The volume intends to show the historicaldevelopment of this important area of formal reasoning up to itscurrent state of art and appears in honor of Peter Andrews on his 70thbirthday.