L.Brugnano and J.R.Cash For a number of years this special issue of JNAIAM has been devoted to the proceedings of the ICNAAM Conference series. In particular the seventh conference, held in Rethymno, Crete (GR), from 18th to 22th September 2009, celebrates the 60th birthday of Professor Ernst Hairer. As is well known, Ernst is one of the leading experts in the numerical solution of ODEs. He has contributed substantially to the field, both in the theoretical analysis of numerical methods, and from the point of view of software development. He is coauthor of a number of monographs on this topic, as well as of some of the most reliable codes for stiff ODEs, based on Radau IIA formulae. One of the fields where he has been very involved in the last few years is that of geometric numerical integration, where he is coauthor, with Christian Lubich and Gerard Wanner, of one of the most comprehensive monographs on the subject.