This book is a collection of papers that have been presented at the International Seminars on Mathematical Music Theory and Music Informatics¹ in Mexico (2000), Sauen (2001) and Zurich (October 2002). The book is also a significant trace of related collaborative work estabished since the early nineties of the last century. This collaboration was organized by the IFM association. A short history of this organization is prepended to the scientific contributions.
There are various cross-references between several papers of this book which trace mutual influences and inspirations as well as collaborations. The aim of this introductory text is to shed light on these connections in order to provide the reader with some orientational grid points.
Behind the editors’ choice of the linear order among the book’s contributions there is a practical grouping following two criteria, namely (1) whether the investigations put their emphasis on a metalevel or on an object level with respect to the underlying music-theoretical interpretations and (2) whether software development or usage plays a significant role in the paper.

The first three texts are contributions of introductory nature in behalf of the three editors of this book. Thomas Noll’s contribution Vade Mecum to Mathematical Music Theory invites the reader to an exciting transdisciplinary research domain on the basis of historical and common sense remarks and simple examples. In Music and Mathematics: two »Fine Arts«, Emilio Lluis-Puebla, who is both, a professor for mathematics and a concert pianist, explores the two fields of his parallel professional careers starting from a comparison of mathematical and musical creativity. The text is based on a lecture held 2001 at the seminar in Sauen. Guerino Mazzola’s text Mathematical Music Theory--Status Quo 2000 draws the balance of his own work and related research, it was delivered as a lecture in 2000 in Mexico and hence provides information about developments preceeding the three seminars.

A next group comprises five contributions which are devoted to theoretical metalanguage investigations. The papers Towards a Galois Theory of Concepts by Guerino Mazzola and The Denotator: Its Structure, Construction, and Role in Mathematical Music Theory by Mariana Montiel are concerned with the principles of concept architectures for musical structures. Both papers are based on Mazzola’s denotator theory. Montiel reviews basic definitions and explains them on the basis of examples. Mazzola is concerned with the creation of denotators as >solutions