The semi simple zeta function of quaternionic Shimura varieties This monograph is concerned with the Shimura variety attached to a quaternion algebra over a totally real number field. For any place of good (or moderately bad) reduction the corresponding (semi simple) local zeta function is expressed in terms of (semi simple) local L functions attached to automorphic representations. In an appendix a conjecture of Langlands and Rapoport on the reduction of a Shimura variety in a very general case is restated in a slightly stronger form. The reader is expected to be familiar with the basic concepts of algebraic geometry algebraic number theory and the theory of automorphic representation