The conference "Phenomena in High Dimensions" will take place in Samos, Greece, from June 25-29, 2007. It is the third annual conference of the Marie Curie Research Training Network "Phenomena in High Dimensions" (MRTN-CT-2004-511953). It is supported by the European Community's Sixth Framework Programme. Alexander S. Onassis, Public Benefit Foundation. Municipality of Pythagorion. the Departments of Mathematics of the University of the Aegean and the University of Athens. Members of the network as well as all other interested mathematicians are invited to participate.  The goal of this conference is to present and discuss recent research and results in Asymptotic Geometric Analysis, Convex Geometry, Asymptotic Combinatorics, Isoperimetric Principles in Geometry and Probability, and related areas with particular emphasis on High-dimensional Phenomena. The conference will include a young researchers meeting.