This book constitutes the thoroughly refereed research papers contributed to a research project on the 'General Theory of Information Transfer and Combinatorics' that was hosted from 2001-2004 at the Center for Interdisciplinary Research (ZIF) of Bielefeld University and also papers of several incorporated meetings thereof. The 63 revised full papers presented were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on probabilistic models, cryptology, pseudo random sequences, quantum models, statistics, probability theory, information measures, error concepts, performance criteria, search, sorting, ordering, planning, language evolution, pattern discovery, reconstructions, network coding, combinatorial models, and a problem section.

The lectures concentrate on highlights in Combinatorial (ChaptersII and III) and Number Theoretical (ChapterIV) Extremal Theory, in particular on the solution of famous problems which were open for many decades. However, the organization of the lectures in six chapters does neither follow the historic developments nor the connections between ideas in several cases. With the speci?ed auxiliary results in ChapterI on Probability Theory, Graph Theory, etc., all chapters can be read and taught independently of one another. In addition to the 16 lectures organized in 6 chapters of the main part of the book, there is supplementary material for most of them in the Appendix. In parti- lar, there are applications and further exercises, research problems, conjectures, and even research programs. The following books and reports [B97], [ACDKPSWZ00], [A01], and [ABCABDM06], mostly of the authors, are frequently cited in this book, especially in the Appendix, and we therefore mark them by short labels as [B], [N], [E], and [G]. We emphasize that there are also “Exercises” in [B], a “Problem Section” with contributions by several authors on pages 1063–1105 of [G], which are often of a combinatorial nature, and “Problems and Conjectures” on pages 172–173 of [E].

This book constitutes the thoroughly refereed research papers contributed to a research project on the 'General Theory of Information Transfer and Combinatorics' that was hosted from 2001-2004 at the Center for Interdisciplinary Research (ZIF) of Bielefeld University and also papers of several incorporated meetings thereof. The 63 revised full papers presented were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on probabilistic models, cryptology, pseudo random sequences, quantum models, statistics, probability theory, information measures, error concepts, performance criteria, search, sorting, ordering, planning, language evolution, pattern discovery, reconstructions, network coding, combinatorial models, and a problem section.

The lectures concentrate on highlights in Combinatorial (ChaptersII and III) and Number Theoretical (ChapterIV) Extremal Theory, in particular on the solution of famous problems which were open for many decades. However, the organization of the lectures in six chapters does neither follow the historic developments nor the connections between ideas in several cases. With the speci?ed auxiliary results in ChapterI on Probability Theory, Graph Theory, etc., all chapters can be read and taught independently of one another. In addition to the 16 lectures organized in 6 chapters of the main part of the book, there is supplementary material for most of them in the Appendix. In parti- lar, there are applications and further exercises, research problems, conjectures, and even research programs. The following books and reports [B97], [ACDKPSWZ00], [A01], and [ABCABDM06], mostly of the authors, are frequently cited in this book, especially in the Appendix, and we therefore mark them by short labels as [B], [N], [E], and [G]. We emphasize that there are also “Exercises” in [B], a “Problem Section” with contributions by several authors on pages 1063–1105 of [G], which are often of a combinatorial nature, and “Problems and Conjectures” on pages 172–173 of [E].