The papers included in this volume provide an overview about thestate-of-the-art in approximative implicitization and various relatedtopics, including both the theoretical basis and the existingcomputational techniques.  The novel idea of approximateimplicitization has strengthened the existing link between ComputerAided Geometric Design and classical algebraic geometry. There is agrowing interest from researchers and professionals both in CAGD andAlgebraic Geometry, to meet and combine knowledge and ideas, in orderto better solve industrial--type challenges, as well as to initiate newdirections for basic research. This volume will support this exchangeof ideas between the various communities.