During the last 15 years spectacular advances have been made in controlling quantum systems composed of atomic constituents, revolutionizing the field of traditional atomic, molecular, and optical (AMO) physics and opening up new and spectacular avenues in such diverse areas as precision spectroscopy, quantum information, quantum many-body and condensed matter physics. The challenge is now to reach the same level of control in molecular systems, for which the presence of additional microscopic degrees of freedom promises a new era for quantum physics and chemistry. In this emerging, strongly multi-disciplinary field, challenges range from the production of cold and ultracold molecules to the application of these cold and ultracold molecules to precision spectroscopy, few-body and many-body quantum physics, chemical physics, and quantum chemistry. It is the aim of this conference to bring together scientists from these diverse fields, which are now contributing to an increasing extent to developing new ideas and approaches for the realization of cold and ultracold molecular gases and to identifying new research directions and applications of these novel systems. This conference will be structured to initiate and foster intensive collaborations, in particular between theory and experiment, which will be an essential ingredient for the overall progress of this interdisciplinary field.