Mathematics for computation (M4C) The overall topic of the volume Mathematics for Computation (M4C) is mathematics taking crucially into account the aspect of computation investigating the interaction of mathematics with computation bridging the gap between mathematics and computation wherever desirable and possible and otherwise explaining why not. Recently abstract mathematics has proved to have more computational content than ever expected. Indeed the axiomatic method originally intended to do away with concrete computations seems to suit surprisingly well the programs from proofs paradigm with abstraction helping not only clarity but also efficiency. Unlike computational mathematics which rather focuses on objects of computational nature such as algorithms the scope of M4C generally encompasses all the mathematics including abstract concepts such as functions. The purpose of M4C actually is a strongly theory based and therefore is a more reliable and sustainable approach to actual computation up to the systematic development of verified software. While M4C is situated within mathematical logic and the related area of theoretical computer science in principle it involves all branches of mathematics especially those which prompt computational considerations. In traditional terms the topics of M4C include proof theory constructive mathematics complexity theory reverse mathematics type theory category theory and domain theory. The aim of this volume is to provide a point of reference by presenting up to date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross fertilization between different styles and traditions