Information Geometry and Algebraic Statistics are brought together in this volume to suggest that the interaction between them is possible and auspicious.

To meet this aim, we couple expository material with more advanced research topics sometimes within the same chapter, cross-reference the various chapters, and include many examples both in the printed volume and in the on-line supplement, held at the Cambridge University Press web site at www.cambridge.org/9780521896191. The on-line part includes proofs that are instructive but long or repetitive, computer codes and detailed development of special cases.

Chapter 1 gives a brief introduction to both Algebraic Statistics and Information Geometry based on the simplest possible examples and on selected topics that, to the editors, seem most promising for the interlacing between them. Then, the volume splits naturally in two lines. Part I, on contingency tables, and Part II, on designed experiments, are authored by researchers active mainly within Algebraic Statistics, while Part III includes chapters on both classical and quantum Information Geometry. This material comes together in Part IV which consists of only one chapter by Giovanni Pistone, to whom the volume is dedicated, and provides examples of the interplay between Information Geometry and Algebraic Statistics.