The papers included in this volume provide an overview of the state of the art in approximative implicitization and various related topics, including both the theoretical basis and the existing computational techniques.The novel idea of approximate implicitization has strengthened the existing link between Computer Aided Geometric Design and classical algebraic geometry. There is a growing interest from researchers and professionals both in CAGD and Algebraic Geometry, to meet andcombine knowledge and ideas,with the aim to improve the solving of industrial-type challenges, as well as to initiate new directions for basic research. This volume will support this exchange of ideas between the various communities.