This collection of articles is published in honour of Rudolf Ahlswede. His main areas of research are represented in the three sections, "Numbers and Combinations", "Information Theory" (channels and networks, combinatorial and algebraic coding, cryptology, with the related fields data compression, entropy theory, symbolic dynamics, probability and statistics), and "Complexity". Special attention was paid to the interplay between the fields. Surveys on topics of current interest are included as well as new research results. The book features surveys on combinatorics about topics such as intersection theorems, which are not yet covered in textbooks, several contributions by leading experts in data compression, and relations to natural sciences are discussed.